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Journal articles on the topic 'Mellin Barnes'

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Published: 6 September 2023

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1

Baumann, Gerd, and Norbert Südland. "Sinc Numeric Methods for Fox-H, Aleph (ℵ), and Saxena-I Functions." Fractal and Fractional 6, no. 8 (August 18, 2022): 449. http://dx.doi.org/10.3390/fractalfract6080449.

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The purpose of this study is to offer a systematic, unified approach to the Mellin-Barnes integrals and associated special functions as Fox H, Aleph ℵ, and Saxena I function, encompassing the fundamental features and important conclusions under natural minimal assumptions on the functions in question. The approach’s pillars are the concept of a Mellin-Barnes integral and the Mellin representation of the given function. A Sinc quadrature is used in conjunction with a Sinc approximation of the function to achieve the numerical approximation of the Mellin-Barnes integral. The method converges exponentially and can handle endpoint singularities. We give numerical representations of the Aleph ℵ and Saxena I functions for the first time.

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2

Kumar, Hemant. "CERTAIN RESULTS OF GENERALIZED BARNES TYPE DOUBLE SERIES RELATED TO THE HURWITZ-LERCH ZETA FUNCTIONS OF TWO VARIABLES." jnanabha 52, no. 02 (2022): 191–201. http://dx.doi.org/10.58250/jnanabha.2022.52222.

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In these researches we introduce a generalized Barnes type double series and then, discuss its convergent conditions. We obtain some of its results related to the known and new Hurwitz -Lerch zeta function of two variables and also derive Eulerian and Mellin- Barnes type integral representations of these functions and analyze various properties these functions

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3

Matsumoto, Kohji. "Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series." Nagoya Mathematical Journal 172 (2003): 59–102. http://dx.doi.org/10.1017/s0027763000008643.

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AbstractThe present paper contains three main results. The first is asymptotic expansions of Barnes double zeta-functions, and as a corollary, asymptotic expansions of holomorphic Eisenstein series follow. The second is asymptotic expansions of Shintani double zeta-functions, and the third is the analytic continuation of n-variable multiple zeta-functions (or generalized Euler-Zagier sums). The basic technique of proving those results is the method of using the Mellin-Barnes type of integrals.

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4

Yakubovich, S. B., and Shyam L. Kalla. "On a new approach to convolution constructions." International Journal of Mathematics and Mathematical Sciences 16, no. 3 (1993): 435–48. http://dx.doi.org/10.1155/s0161171293000559.

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In this paper we establish some new approach to constructing convolution for general Mellin type transforms. This method is based on the theory of double Hellin-Barnes integrals. Some properties of convolutions and several examples are given.

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5

Temme, Nico M. "Book Review: Asymptotics and Mellin-Barnes integrals." Mathematics of Computation 71, no. 240 (2002): 1799. http://dx.doi.org/10.1090/s0025-5718-02-01500-4.

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6

Kharchev, S., and S. Khoroshkin. "Mellin-Barnes presentations for Whittaker wave functions." Advances in Mathematics 375 (December 2020): 107368. http://dx.doi.org/10.1016/j.aim.2020.107368.

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7

Czakon, M. "Automatized analytic continuation of Mellin–Barnes integrals." Computer Physics Communications 175, no. 8 (October 2006): 559–71. http://dx.doi.org/10.1016/j.cpc.2006.07.002.

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8

Elizalde, E., K. Kirsten, and S. Zerbini. "Applications of the Mellin-Barnes integral representation." Journal of Physics A: Mathematical and General 28, no. 3 (February 7, 1995): 617–29. http://dx.doi.org/10.1088/0305-4470/28/3/016.

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9

Krefl, Daniel. "Mellin–Barnes Representation of the Topological String." Letters in Mathematical Physics 106, no. 11 (August 23, 2016): 1561–74. http://dx.doi.org/10.1007/s11005-016-0882-2.

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10

Borisov, Lev A., and R. Paul Horja. "Mellin–Barnes integrals as Fourier–Mukai transforms." Advances in Mathematics 207, no. 2 (December 2006): 876–927. http://dx.doi.org/10.1016/j.aim.2006.01.011.

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11

García, Héctor Luna, and Luz María García. "Feynman integrals and hypergeometric functions." International Journal of Modeling, Simulation, and Scientific Computing 05, supp01 (October 2014): 1441001. http://dx.doi.org/10.1142/s1793962314410013.

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We review Davydychev method for calculating Feynman integrals for massive and no massive propagators, by employing Mellin–Barnes transformation and the dimensional regularization scheme, same that lead to hypergeometric functions. In particular, an example is calculated explicitly from such a method.

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12

Al-Musallam, Fadhel A., and Vu Kim Tuan. "H-function with complex parameters I: existence." International Journal of Mathematics and Mathematical Sciences 25, no. 9 (2001): 571–86. http://dx.doi.org/10.1155/s0161171201005142.

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AnH-function with complex parameters is defined by a Mellin-Barnes type integral. Necessary and sufficient conditions under which the integral defining theH-function converges absolutely are established. Some properties, special cases, and an application to integral transforms are given.

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13

Helversen-Pasotto, Anna, and Patrick Solé. "Barnes' First Lemma and its Finite Analogue." Canadian Mathematical Bulletin 36, no. 3 (September 1, 1993): 273–82. http://dx.doi.org/10.4153/cmb-1993-039-1.

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AbstractWe give a parallel proof of Barnes' first lemma and of its finite analogue. In both cases we use the Mellin transform. In the classical case, the proof avoids the residue theorem. In the finite case the Gamma function is replaced by the Gaussian sum function and the beta function by the Jacobi sum function.

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14

VALTANCOLI, P. "THE SCALAR BOX INTEGRAL AND THE MELLIN–BARNES REPRESENTATION." International Journal of Modern Physics A 26, no. 15 (June 20, 2011): 2557–68. http://dx.doi.org/10.1142/s0217751x11053444.

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We solve exactly the scalar box integral using the Mellin–Barnes representation. First we recognize the hypergeometric functions resumming the series coming from the scalar integrals, then we perform an analytic continuation before applying the Laurent expansion in ϵ = (d-4)/2 of the result.

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15

Ostrovsky, Dmitry. "On Barnes beta distributions, Selberg integral and Riemann xi." Forum Mathematicum 28, no. 1 (January 1, 2016): 1–23. http://dx.doi.org/10.1515/forum-2013-0149.

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AbstractThe theory of Barnes beta probability distributions is advanced and related to the Riemann xi function. The scaling invariance, multiplication formula, and Shintani factorization of Barnes multiple gamma functions are reviewed using the approach of Ruijsenaars and shown to imply novel properties of Barnes beta distributions. The applications are given to the meromorphic extension of the Selberg integral as a function of its dimension and the scaling invariance of the underlying probability distribution. This probability distribution in the critical case is described and conjectured to be the distribution of the derivative martingale. The Jacobi triple product is interpreted probabilistically resulting in an approximation of the Riemann xi function by the Mellin transform of the logarithm of a limit of Barnes beta distributions.

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16

Ostrovsky, Dmitry. "A review of conjectured laws of total mass of Bacry–Muzy GMC measures on the interval and circle and their applications." Reviews in Mathematical Physics 30, no. 10 (October 12, 2018): 1830003. http://dx.doi.org/10.1142/s0129055x18300030.

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Selberg and Morris integral probability distributions are long conjectured to be distributions of the total mass of the Bacry–Muzy Gaussian Multiplicative Chaos measures with non-random logarithmic potentials on the unit interval and circle, respectively. The construction and properties of these distributions are reviewed from three perspectives: Analytic based on several representations of the Mellin transform, asymptotic based on low intermittency expansions, and probabilistic based on the theory of Barnes beta probability distributions. In particular, positive and negative integer moments, infinite factorizations and involution invariance of the Mellin transform, analytic and probabilistic proofs of infinite divisibility of the logarithm, factorizations into products of Barnes beta distributions, and Stieltjes moment problems of these distributions are presented in detail. Applications are given in the form of conjectured mod-Gaussian limit theorems, laws of derivative martingales, distribution of extrema of [Formula: see text] noises, and calculations of inverse participation ratios in the Fyodorov–Bouchaud model.

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17

Agarwal, Praveen, Jessada Tariboon, and Shilpi Jain. "New Bilateral Type Generating Function Associated withI-Function." Abstract and Applied Analysis 2014 (2014): 1–3. http://dx.doi.org/10.1155/2014/157297.

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We aim at establishing a new bilateral type generating function associated with theI-function and a Mellin-Barnes type of contour integral. The results derived here are of general character and can yield a number of (known and new) results in the theory of generating functions.

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18

Friot, Samuel, and David Greynat. "On convergent series representations of Mellin-Barnes integrals." Journal of Mathematical Physics 53, no. 2 (February 2012): 023508. http://dx.doi.org/10.1063/1.3679686.

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19

Allendes, Pedro, Natanael Guerrero, Igor Kondrashuk, and Eduardo A. Notte Cuello. "New four-dimensional integrals by Mellin–Barnes transform." Journal of Mathematical Physics 51, no. 5 (May 2010): 052304. http://dx.doi.org/10.1063/1.3357105.

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20

Smirnov, V. A. "Evaluating multiloop Feynman integrals by Mellin-Barnes representation." Nuclear Physics B - Proceedings Supplements 135 (October 2004): 252–56. http://dx.doi.org/10.1016/j.nuclphysbps.2004.09.024.

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21

MATSUBARA-HEO, Saiei-Jaeyeong. "ON MELLIN-BARNES INTEGRAL REPRESENTATIONS FOR GKZ HYPERGEOMETRIC FUNCTIONS." Kyushu Journal of Mathematics 74, no. 1 (2020): 109–25. http://dx.doi.org/10.2206/kyushujm.74.109.

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22

Dubovyk, I., J. Gluza, and T. Riemann. "Optimizing the Mellin--Barnes Approach to Numerical Multiloop Calculations." Acta Physica Polonica B 50, no. 11 (2019): 1993. http://dx.doi.org/10.5506/aphyspolb.50.1993.

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23

Mainardi, Francesco, and Gianni Pagnini. "Salvatore Pincherle: the pioneer of the Mellin–Barnes integrals." Journal of Computational and Applied Mathematics 153, no. 1-2 (April 2003): 331–42. http://dx.doi.org/10.1016/s0377-0427(02)00609-x.

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24

Allendes, Pedro, Bernd A. Kniehl, Igor Kondrashuk, Eduardo A. Notte-Cuello, and Marko Rojas-Medar. "Solution to Bethe–Salpeter equation via Mellin–Barnes transform." Nuclear Physics B 870, no. 1 (May 2013): 243–77. http://dx.doi.org/10.1016/j.nuclphysb.2013.01.012.

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25

Kniehl, Bernd A., Igor Kondrashuk, Eduardo A. Notte-Cuello, Ivan Parra-Ferrada, and Marko Rojas-Medar. "Two-fold Mellin–Barnes transforms of Usyukina–Davydychev functions." Nuclear Physics B 876, no. 1 (November 2013): 322–33. http://dx.doi.org/10.1016/j.nuclphysb.2013.08.002.

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26

Friot, Samuel, David Greynat, and Eduardo de Rafael. "Asymptotics of Feynman diagrams and the Mellin–Barnes representation." Physics Letters B 628, no. 1-2 (November 2005): 73–84. http://dx.doi.org/10.1016/j.physletb.2005.08.126.

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27

Paris, R. B. "Smoothing of the Stokes phenomenon using Mellin-Barnes integrals." Journal of Computational and Applied Mathematics 41, no. 1-2 (August 1992): 117–33. http://dx.doi.org/10.1016/0377-0427(92)90242-p.

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28

Sidorov, Alexander, Olga Solovtsova, and Vasil Lashkevich. "High-precision numerical estimates of the Mellin-Barnes integrals for the structure functions based on the stationary phase contour." EPJ Web of Conferences 204 (2019): 02008. http://dx.doi.org/10.1051/epjconf/201920402008.

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We present a recipe for constructing the effcient contour which allows one to calculate with high accuracy the Mellin-Barnes integrals, in particular, for the F3 structure function written in terms of its Mellin moments. We have demonstrated that the contour of the stationary phase arising for the F3 structure function tends to the finite limit as Re(z) → –∞. We show that the Q2 evolution of the structure function can be represented as an integral over the contour of the stationary phase within the framework of the Picard-Lefschetz theory. The universality of the asymptotic contour of the stationary phase defined at some fixed value of the momentum transfer square $Q_{0}^{2}$ for calculations with any Q2 is shown.

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29

Choi, Junesang, and Rakesh Parmar. "An extension of the generalized Hurwitz-Lerch Zeta function of two variables." Filomat 31, no. 1 (2017): 91–96. http://dx.doi.org/10.2298/fil1701091c.

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The main object of this paper is to introduce a new extension of the generalized Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate such its several interesting properties and related formulas as (for example) various integral representations, which provide certain new and known extensions of earlier corresponding results, a summation formula and Mellin-Barnes type contour integral representations. We also consider some important special cases.

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30

Smirnov, A. V., and V. A. Smirnov. "On the resolution of singularities of multiple Mellin–Barnes integrals." European Physical Journal C 62, no. 2 (May 5, 2009): 445–49. http://dx.doi.org/10.1140/epjc/s10052-009-1039-6.

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31

Kharchev, S., and D. Lebedev. "Eigenfunctions of GL(N, ℝ) Toda chain: Mellin-Barnes representation." Journal of Experimental and Theoretical Physics Letters 71, no. 6 (March 2000): 235–38. http://dx.doi.org/10.1134/1.568323.

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32

Friot, Samuel, and David Greynat. "Asymptotic expansions of Feynman diagrams and the Mellin-Barnes representation." Nuclear Physics B - Proceedings Supplements 164 (February 2007): 199–202. http://dx.doi.org/10.1016/j.nuclphysbps.2006.11.060.

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33

Khushtova, F. G. "On the Mellin–Barnes integral representation of one special function." News of the Kabardin-Balkar Scientific Center of RAS 6, no. 110 (2022): 19–27. http://dx.doi.org/10.35330/1991-6639-2022-6-110-19-27.

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34

Desai, Rachana, and A. K. Shukla. "Note on the <i><sub>p</sub>R<sub>q</sub>(Î±; Î²; z)</i> Function." Journal of the Indian Mathematical Society 88, no. 3-4 (June 14, 2021): 288. http://dx.doi.org/10.18311/jims/2021/27835.

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The aim of this paper is to give some convergence conditions of the <em><sub>p</sub>R<sub>q</sub>(Î±; Î²; z)</em> function. We also derive the integral representation of the function <em><sub>p</sub>R<sub>q</sub>(Î±; Î²; z)</em> in the form of Mellin-Barnes Integral including its analytic property.

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35

Mehrez, Khaled, and Zivorad Tomovski. "On a new (p,q)-Mathieu-type power series and its applications." Applicable Analysis and Discrete Mathematics 13, no. 1 (2019): 309–24. http://dx.doi.org/10.2298/aadm190427005m.

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Our aim in this paper, is to establish certain new integral representations for the (p,q)-Mathieu-type power series. In particular, we investigate the Mellin-Barnes type integral representations for a particular case of these special function. Moreover, we introduce the notion of the (p, q)-Mittag- Leffler functions and we present a relationships between these two functions. Some other applications are proved, in particular two Tur?n type inequalities for the (p,q)-Mathieu-type series are derived.

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36

Aguilar, Jean-Philippe, Cyril Coste, and Jan Korbel. "Series representation of the pricing formula for the European option driven by space-time fractional diffusion." Fractional Calculus and Applied Analysis 21, no. 4 (August 28, 2018): 981–1004. http://dx.doi.org/10.1515/fca-2018-0054.

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Abstract In this paper, we show that the price of an European call option, whose underlying asset price is driven by the space-time fractional diffusion, can be expressed in terms of rapidly convergent double-series. This series formula is obtained from the Mellin-Barnes representation of the option price with help of residue summation in ℂ2. We also derive the series representation for the associated risk-neutral factors, obtained by Esscher transform of the space-time fractional Green functions.

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37

Moriyama, Tomonori. "Spherical Functions for the Semisimple Symmetric Pair (Sp(2, ℝ), SL(2, ℂ))." Canadian Journal of Mathematics 54, no. 4 (August 1, 2002): 828–65. http://dx.doi.org/10.4153/cjm-2002-032-2.

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AbstractLet π be an irreducible generalized principal series representation of G = Sp(2, ℝ) induced from its Jacobi parabolic subgroup. We show that the space of algebraic intertwining operators from π to the representation induced from an irreducible admissible representation of SL(2, ℂ) in G is at most one dimensional. Spherical functions in the title are the images of K-finite vectors by this intertwining operator. We obtain an integral expression of Mellin-Barnes type for the radial part of our spherical function.

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38

Oli, Abdi, Kelelaw Tilahun, and G. V. Reddy. "The Multivariable Aleph-function involving the Generalized Mellin-Barnes Contour Integrals." Cubo (Temuco) 22, no. 3 (December 2020): 351–59. http://dx.doi.org/10.4067/s0719-06462020000300351.

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39

Ayant, Frederic. "On Unification of Generalized Functions Representable by Mellin-Barnes Contour Integrals." International Journal of Mathematics Trends and Technology 62, no. 1 (October 25, 2018): 67–74. http://dx.doi.org/10.14445/22315373/ijmtt-v62p510.

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40

Bierenbaum, Isabella, Johannes Blümlein, and Sebastian Klein. "Evaluating Two-Loop massive Operator Matrix Elements with Mellin-Barnes Integrals." Nuclear Physics B - Proceedings Supplements 160 (October 2006): 85–90. http://dx.doi.org/10.1016/j.nuclphysbps.2006.09.033.

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41

Zhdanov, O. N., and A. K. Tsikh. "Studying the multiple Mellin-Barnes integrals by means of multidimensional residues." Siberian Mathematical Journal 39, no. 2 (April 1998): 245–60. http://dx.doi.org/10.1007/bf02677509.

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42

Srinivasan, Gopala Krishna. "A unified approach to the integrals of Mellin–Barnes–Hecke type." Expositiones Mathematicae 31, no. 2 (2013): 151–68. http://dx.doi.org/10.1016/j.exmath.2013.01.008.

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43

Dubovyk, Ievgen, Janusz Gluza, and Tord Riemann. "Non-planar Feynman diagrams and Mellin-Barnes representations with AMBRE 3.0." Journal of Physics: Conference Series 608 (May 22, 2015): 012070. http://dx.doi.org/10.1088/1742-6596/608/1/012070.

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44

Bytsenko, A. A., E. Elizalde, S. D. Odintsov, and S. Zerbini. "Mellin-Barnes representation for the genus-g finite temperature string theory." Physics Letters B 311, no. 1-4 (July 1993): 87–92. http://dx.doi.org/10.1016/0370-2693(93)90538-s.

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45

Cohl, Howard S., and Roberto S. Costas-Santos. "Nonterminating transformations and summations associated with some q-Mellin–Barnes integrals." Advances in Applied Mathematics 147 (June 2023): 102517. http://dx.doi.org/10.1016/j.aam.2023.102517.

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46

Khushtova, F. G. "On some formulas for fractional integration of one Fox function with four parameters." ADYGHE INTERNATIONAL SCIENTIFIC JOURNAL 22, no. 4 (2022): 29–38. http://dx.doi.org/10.47928/1726-9946-2022-22-4-29-38.

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Solutions to many problems of mathematical physics, engineering and economics arc expressed through the so-called special functions. In the theory of special functions an important place is occupied by functions of the hypergeometric type. Many of them can be written in terms of the Meyer G-function. A generalization of the Meyer function is the Fox H-function. Some properties of this function can be obtained from its representation using the Mellin – Barnes integral. When deriving some formulas for this function for particular values of its parameters, due to the cumbersome writing of the Fox function, it is more convenient to use simplified notation. In this paper, we consider a special case of such a Fox function containing four parameters. For this function, Riemann-Liouville and Erdelyi-Kober fractional integration formulas arc obtained. An integral representation of the considered function h through the Mellin – Burns integral, we write out the conditions under which it converges absolutely, and the asymptotic expansions for this function for large and small values of the argument. The formulas proved in the paper are obtained using the indicated Mellin – Burns integral representation and the well-known integration formulas from power functions. For particular values of the parameters, the function under consideration yields some well-known elementary and special functions, and from the obtained formulas of fractional integration – the known integral values of these functions.

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47

Gu, Zhi-Hua, Hai-Bin Zhang, and Tai-Fu Feng. "Hypergeometric expression for a three-loop vacuum integral." International Journal of Modern Physics A 35, no. 19 (July 8, 2020): 2050089. http://dx.doi.org/10.1142/s0217751x2050089x.

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Using the corresponding Mellin–Barnes representation, we derive holonomic hypergeometric system of linear partial differential equations (PDEs) satisfied by Feynman integral of a three-loop vacuum with five propagators. Through the multidimensional residue theorem in dimensional regularization, the scalar integral can be written as the summation of multiple hypergeometric functions, whose convergent regions can be obtained by the Horn’s convergent theory. The numerical continuation of the scalar integral from convergent regions to whole kinematic regions can be accomplished with the finite element methods, when the system of PDEs can be treated as the stationary conditions of a functional under the restrictions.

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48

Kilbas, Anatoly A., and Megumi Saigo. "On the H-function." Journal of Applied Mathematics and Stochastic Analysis 12, no. 2 (January 1, 1999): 191–204. http://dx.doi.org/10.1155/s1048953399000192.

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This paper is devoted to the study of the H-function as defined by the Mellin-Barnes integral Hp,qm,n(z)=12πi∫ℒℋp,qm,n(s)z−sds, where the function ℋp,qm,n(s) is a certain ratio of products of the Gamma-functions with the argument s and the contour ℒ specially chosen. The conditions for the existence of Hp,qm,n(z) are discussed and explicit power and power-logarithmic series expansions of Hp,qm,n(z) near zero and infinity are given. The obtained results define more precisely the known results.

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49

Lindqvist, Gunilla. "LEKENS ESTETIK." Psyke & Logos 23, no. 2 (December 1, 2002): 14. http://dx.doi.org/10.7146/pl.v23i2.8598.

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Syftet med studien är att undersöka lek och kulturella estetiska mönster för att kunna utveckla en skapande lekpedagogik för att förstå den potentiella utvecklingen av barns lek för att de skall skapa mening. Med utgångspunkt i Vygotskijs kulturhistoriska teori om dramapedagogisk teori och litteratur utvecklas ett synsätt på lek, där det finns ett dynamiskt samband mellan barnens lek och omgivningens kulturella påverkan. Studien innehåller ett didaktiskt försök (utvecklingsexperiment) på en förskola i Karlstad, med ett lektema, där berättelsen är den röda tråden och där vi använder dramapedagogiska metoder och utgår från lekens form. Metoden var att analysera texter kvalitativt, både dramatiseringar och barnens lekar (videofilmade) och den pedagogiska analysen handlade om reflektera över den dynamiska relationen mellan lek och kultur. Resultaten visar att en gemensam LEKVÄRLD hjälper till att utveckla barns lek på förskolan. Barnen skapade mening på en hel situation. När de vuxna dramatiserade karaktärer och handlingar så etablerades en dialog med barnen, där de vuxna förde barnen in i fiktionen. VÄRLD, HANDLING och KARAKTÄRER hör ihop i barns lek och barn skapar MENING vilket förbereder för abstrakt tänkande, konstnärlig och en kreativ förmåga.

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50

Kaminski, D., and R. B. Paris. "Asymptotics via iterated Mellin–Barnes integrals: Application to the generalised Faxén integral." Methods and Applications of Analysis 4, no. 3 (1997): 311–25. http://dx.doi.org/10.4310/maa.1997.v4.n3.a5.

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