Literatura académica sobre el tema "Bernoulli number"
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Artículos de revistas sobre el tema "Bernoulli number"
Chen, Kwang-Wu. "Median Bernoulli Numbers and Ramanujan’s Harmonic Number Expansion". Mathematics 10, n.º 12 (12 de junio de 2022): 2033. http://dx.doi.org/10.3390/math10122033.
Texto completoJakimczuk, Rafael. "Sequences related to the e number and Bernoulli numbers". Gulf Journal of Mathematics 11, n.º 1 (9 de agosto de 2021): 38–42. http://dx.doi.org/10.56947/gjom.v11i1.666.
Texto completoRawlings, Don. "Bernoulli Trials and Number Theory". American Mathematical Monthly 101, n.º 10 (diciembre de 1994): 948. http://dx.doi.org/10.2307/2975160.
Texto completoRawlings, Don. "Bernoulli Trials and Number Theory". American Mathematical Monthly 101, n.º 10 (diciembre de 1994): 948–52. http://dx.doi.org/10.1080/00029890.1994.12004573.
Texto completoKaneko, Masanobu. "Poly-Bernoulli numbers". Journal de Théorie des Nombres de Bordeaux 9, n.º 1 (1997): 221–28. http://dx.doi.org/10.5802/jtnb.197.
Texto completoGradl, Hans y Sebastian Walcher. "Bernoulli algebras". Communications in Algebra 21, n.º 10 (enero de 1993): 3503–20. http://dx.doi.org/10.1080/00927879308824745.
Texto completoCaratelli, Diego, Pierpaolo Natalini y Paolo Emilio Ricci. "Fractional Bernoulli and Euler Numbers and Related Fractional Polynomials—A Symmetry in Number Theory". Symmetry 15, n.º 10 (10 de octubre de 2023): 1900. http://dx.doi.org/10.3390/sym15101900.
Texto completoCRABB, M. C. "THE MIKI-GESSEL BERNOULLI NUMBER IDENTITY". Glasgow Mathematical Journal 47, n.º 2 (27 de julio de 2005): 327–28. http://dx.doi.org/10.1017/s0017089505002545.
Texto completoXu, Aimin. "Ramanujan’s Harmonic Number Expansion and Two Identities for Bernoulli Numbers". Results in Mathematics 72, n.º 4 (18 de septiembre de 2017): 1857–64. http://dx.doi.org/10.1007/s00025-017-0748-7.
Texto completoKargın, Levent. "p-Bernoulli and geometric polynomials". International Journal of Number Theory 14, n.º 02 (8 de febrero de 2018): 595–613. http://dx.doi.org/10.1142/s1793042118500665.
Texto completoTesis sobre el tema "Bernoulli number"
Chellali, Mustapha. "Congruences, nombres de Bernoulli et polynômes de Bessel". Université Joseph Fourier (Grenoble ; 1971-2015), 1989. http://www.theses.fr/1989GRE10091.
Texto completoWhitaker, Linda M. "The Bernoulli salesman". Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/24935.
Texto completoSmith, Michael J. "Ranking and selection : open sequential procedures for Bernoulli populations". Thesis, Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/25103.
Texto completoMartin, Bruno. "Contribution à la théorie des entiers friables". Phd thesis, Université de Lorraine, 2005. http://tel.archives-ouvertes.fr/tel-00795666.
Texto completoMirkoski, Maikon Luiz. "Números e polinômios de Bernoulli". Universidade Estadual de Ponta Grossa, 2018. http://tede2.uepg.br/jspui/handle/prefix/2699.
Texto completoMade available in DSpace on 2018-11-29T18:07:06Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Maikon Luiz.pdf: 959643 bytes, checksum: aaf472f5b8a9a29532793d01234788a9 (MD5) Previous issue date: 2018-10-19
Neste trabalho,estudamos os números e os polinomios de Bernoulli,bem como algumas de suas aplicações mais importantes em Teoria dos Números. Com base em uma caracterização ao simples, os polinômios de Bernoulli são introduzidos e, posteriormente, os números de Bernoulli. As séries de Fourier dos polinomios de Bernoulli são utilizadas na demonstração da equação funcional da função teta. Esta equação, por sua vez, é utilizada na demonstração da celebre equação funcional da função zeta, que tem importância central na teoria da distribuição dos números primos. Além das conexões com a funções especiais zeta e teta, discutimos também, em detalhe,conexões entre os números e os polinomios de Bernoulli com a função gama. Essas relações são então exploradas para produzir belas fórmulas para certos valores da função zeta, entre outras aplicações.
In this work we study Bernoulli numbers and Bernoulli polynomials, as well as some of its most important applications in Number Theory. Based on a simple characterization, the Bernoulli polynomials are introduced and, later, the Bernoulli numbers. The Fourier series of the Bernoulli polynomials are used to demonstrate the functional equation of the theta function. This equation, in turn, is used in the proof of the famous functional equation of the zeta function, which is central to the theory of prime number distribution. In addition to the connections with the special functions zeta and theta, we also discuss, in detail, connections between the Bernoulli numbers and Bernoulli polynomials with the gamma function. These relations are then explored to produce beautiful formulas for certain values of the zeta function,among other applications.
Stacey, Andrew W. "An Adaptive Bayesian Approach to Bernoulli-Response Clinical Trials". CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd2065.pdf.
Texto completoKondo, Pedro Kiochi. "CÁLCULO FINITO: DEMONSTRAÇÕES E APLICAÇÕES". UNIVERSIDADE ESTADUAL DE PONTA GROSSA, 2014. http://tede2.uepg.br/jspui/handle/prefix/1528.
Texto completoCoordenação de Aperfeiçoamento de Pessoal de Nível Superior
In this work some topics of the Discrete or Finite Calculus are developed. In particular, we study difference operators, factorial powers, Stirling numbers of the first and second type, the Newton’s formula of differences, the fundamental theorem of the Finite Calculus, the summation process, and the Bernoulli numbers and Bernoulli polynomials. Then we show the effectiveness of the theory for the calculation of closed formulas for the value of many finite sums. We also study the classical problem of obtaining the polynomials which express the value of the sums of powers of natural numbers.
Neste trabalho desenvolvemos alguns tópicos do Cálculo Discreto ou Finito. Em particular, estudamos operadores de diferenças, potências fatoriais, números de Stirling do primeiro e do segundo tipo, a fórmula de diferenças de Newton, o teorema fundamental do Cálculo Finito, o processo de somação e os números e polinômios de Bernoulli. Mostramos então a eficácia da teoria no cálculo de fórmulas fechadas para o valor de diversas somas finitas. Também estudamos o problema clássico de obter os polinômios que expressam o valor de somas de potências de números naturais.
Perkins, Rudolph Bronson. "On Special Values of Pellarin’s L-series". The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1383827548.
Texto completoChung, Yi-Shiu y 鍾逸修. "The Calculation and Application of Bernoulli number". Thesis, 2008. http://ndltd.ncl.edu.tw/handle/84502958840518031848.
Texto completo國立臺中教育大學
數學教育學系
96
Up to the present, it is an important study for calculating Bernoulli number. There are many different methods to claculate Bernoulli number. But for these methods, we must take lots of steps to calaulate Bernoulli number. Based on this, our research applies Riemann--zeta function and the extended function of the sums of powers of consecutive integers to get an easier method. Then, we will calculate Bernoulli number by using Matlab 7.1, and investigate the relationship between Bernoulli nmuber and Stirling number of second kind. Our results are as follows. 1. The formula of Bernoulli number is B_{2k}=\frac{1}{2k+1} \left \{ C_{2k}^{2k+1}S_{1}^{\prime}(-1) + \sum_{i=1}^{k}C_{2i+1}^{2k+1} S_{2k-2i}^{\prime}(-1) \right \}, k\in N . 2. When $k$ is bigger, Bernoulli number will become bigger and be alternated between plus and minus. 3. The relationship between Bernoulli number and Stirling number of second kind is B_{m+1}=\sum_{k=1}^{m+1}\frac{(-1)^k}{k+1}\cdot k!\cdot S_2(m+1,k).
Liu, Chih Shiuan y 劉志璿. "The connection between the functions of Riemann zeta and Bernoulli Number". Thesis, 2008. http://ndltd.ncl.edu.tw/handle/17154599310613619902.
Texto completo國立臺中教育大學
數學教育學系
96
This research hung over from the extended functions for the sum of powers of consecutive integers, we colleted the literatures of the related research about the functions of Riemann zeta and Bernoulli Number, both newly interpreted and predigested the properties of the functions of Riemann zeta and Bernoulli Number. Thus we built the connection between the functions of Riemann zeta and Bernoulli Number, according to \zeta(2 k)=(-1)^{k-1} 2^{2k-1} \frac{B_{2k} \pi^{2k}}{(2k)!}, \ k \in \mathbb{N},and S_{2k}^{\prime}(-1)=\frac{(-1)^{k-1} (2k)!}{2^{2k-1} (\pi)^{2k}}\zeta(2k), S_{2k+1}^{\prime}(-1)=0,Take the function of Riemann zeta as bridge, we find that S_{2k}^{\prime}(-1)=B_{2k},B_{2k}=\frac{1}{2k+1} \left \{ C_{2k}^{2k+1} S_{1}^{\prime}(-1)+ \sum_{i=1}^{k} C_{2i+1}^{2k+1} S_{2k-2i}^{\prime}(-1) \right \},where $S_k^{\prime}(x)$ denotes the first derivative of $S_k(x)$ for each positive integer $k$.
Libros sobre el tema "Bernoulli number"
1954-, Dilcher Karl, Skula Ladislav y Slavutskiĭ Ilja Sh, eds. Bernoulli numbers: Bibliography (1713-1990). Kingston, Ont: Queen's University, 1991.
Buscar texto completoArakawa, Tsuneo, Tomoyoshi Ibukiyama y Masanobu Kaneko. Bernoulli Numbers and Zeta Functions. Tokyo: Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2.
Texto completoauthor, Ibukiyama Tomoyoshi, Kaneko Masanobu author y Zagier, Don, 1951- writer of supplementary textual content, eds. Bernoulli numbers and Zeta functions. Tokyo: Springer, 2014.
Buscar texto completoKanemitsu, Shigeru. Vistas of special functions. Singapore: World Scientific, 2007.
Buscar texto completoInvitation to classical analysis. Providence, R.I: American Mathematical Society, 2012.
Buscar texto completoVorlesungen über die Bernoullischen zahlen: Ihren zusammenhang mit den secanten-coefficienten und ihre wichtigeren anwendungen. Berlin: J. Springer, 1991.
Buscar texto completoIbukiyama, Tomoyoshi, Masanobu Kaneko, Tsuneo Arakawa y Don B. Zagier. Bernoulli Numbers and Zeta Functions. Springer, 2016.
Buscar texto completoIbukiyama, Tomoyoshi, Masanobu Kaneko y Tsuneo Arakawa. Bernoulli Numbers and Zeta Functions. Springer, 2014.
Buscar texto completoCapítulos de libros sobre el tema "Bernoulli number"
Ireland, Kenneth y Michael Rosen. "Bernoulli Numbers". En A Classical Introduction to Modern Number Theory, 228–48. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4757-2103-4_15.
Texto completoSimsek, Yilmaz. "Families of Twisted Bernoulli Numbers, Twisted Bernoulli Polynomials, and Their Applications". En Analytic Number Theory, Approximation Theory, and Special Functions, 149–214. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0258-3_6.
Texto completoSándor, J. y B. Crstici. "Stirling, bell, bernoulli, euler and eulerian numbers". En Handbook of Number Theory II, 459–618. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-2547-5_5.
Texto completoIbukiyama, Tomoyoshi y Masanobu Kaneko. "Class Number Formula and an Easy Zeta Function of the Space of Quadratic Forms". En Bernoulli Numbers and Zeta Functions, 155–82. Tokyo: Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_10.
Texto completoWagstaff, Samuel S. "Prime Divisors of the Bernoulli and Euler Numbers". En Number Theory for the Millennium III, 357–74. London: A K Peters/CRC Press, 2023. http://dx.doi.org/10.1201/9780138747022-21.
Texto completoIsaacson, Brad. "Generalized Bernoulli Numbers, Cotangent Power Sums, and Higher-Order Arctangent Numbers". En Combinatorial and Additive Number Theory V, 253–61. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-10796-2_12.
Texto completoAdam, David y Jean-Luc Chabert. "Bhargava’s Exponential Functions and Bernoulli Numbers Associated to the Set of Prime Numbers". En Algebraic, Number Theoretic, and Topological Aspects of Ring Theory, 9–35. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-28847-0_2.
Texto completoChryssaphinou, O., S. Papastavridis y T. Tsapelas. "On the Number of Overlapping Success Runs in a Sequence of Independent Bernoulli Trials". En Applications of Fibonacci Numbers, 103–12. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2058-6_10.
Texto completoIbukiyama, Tomoyoshi y Masanobu Kaneko. "Bernoulli Numbers". En Bernoulli Numbers and Zeta Functions, 1–24. Tokyo: Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_1.
Texto completoRibenboim, Paulo. "Bernoulli Numbers". En Classical Theory of Algebraic Numbers, 367–97. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-0-387-21690-4_18.
Texto completoActas de conferencias sobre el tema "Bernoulli number"
Campos, Richard A., Malvin C. Teich y B. E. A. Saleh. "Homodyne photon-number statistics for nonclassical states of light at a lossless beam splitter". En OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.thii6.
Texto completoDelande, E. D., D. E. Clark y J. Houssineau. "Regional variance in target number: Analysis and application for multi-Bernoulli point processes". En IET Conference on Data Fusion & Target Tracking 2014: Algorithms and Applications. Institution of Engineering and Technology, 2014. http://dx.doi.org/10.1049/cp.2014.0531.
Texto completoKuo, Y. L. y W. L. Cleghorn. "Curvature-Based Finite Element Method for Euler-Bernoulli Beams". En ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34213.
Texto completoChih-Wei Yi, Peng-Jun Wan, Xiang-Yang Li y O. Frieder. "Asymptotic distribution of the number of isolated nodes in wireless ad hoc networks with Bernoulli nodes". En WCNC 2003 - IEEE Wireless Communications and Networking Conference. IEEE, 2003. http://dx.doi.org/10.1109/wcnc.2003.1200623.
Texto completoKatariya, Sumeet, Branislav Kveton, Csaba Szepesvári, Claire Vernade y Zheng Wen. "Bernoulli Rank-1 Bandits for Click Feedback". En Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/278.
Texto completoIshihata, Masakazu y Takanori Maehara. "Exact Bernoulli Scan Statistics using Binary Decision Diagrams". En Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/795.
Texto completoTeng, Shen, Wang Jiong, Sun Dong, Liu Yafeng y Tian Zhouyu. "Modeling and Numerical Simulation of Flow Resistance Characteristics in Slowly-Varying Rectangular Cross-Section Microchannel". En ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65257.
Texto completoCaddemi, Salvatore y Ivo Calio`. "Closed Form Buckling Solutions of Euler-Bernoulli Columns With Multiple Singularities". En ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-11168.
Texto completoYong, Yan. "Vibration of Euler-Bernoulli Beams With Arbitrary Boundaries and Intermediate Constraints". En ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0284.
Texto completoNaguleswaran, S. "Vibration of an Euler-Bernoulli Uniform Beam Carrying Several Thin Disks". En ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48361.
Texto completoInformes sobre el tema "Bernoulli number"
Pengelley, David. Figurate Numbers and Sums of Numerical Powers: Fermat, Pascal, Bernoulli. Washington, DC: The MAA Mathematical Sciences Digital Library, junio de 2013. http://dx.doi.org/10.4169/loci003987.
Texto completoKlammler, Harald. Introduction to the Mechanics of Flow and Transport for Groundwater Scientists. The Groundwater Project, 2023. http://dx.doi.org/10.21083/gxat7083.
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