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Books on the topic 'LEGENDERS FUNCTIONS'

Author: Grafiati

Published: 11 September 2023

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1

Don, Wai Sun. The Chebyshev-Legendre method: implementing Legendre methods on Chebyshev points. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1993.

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2

Iryna, Fedotova, ed. Generalized associated Legendre functions and their applications. Singapore: World Scientific, 2001.

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3

Gottlieb, David. On the Gibbs phenomenon V: Recovering exponential accuracy from collocation point values of a piecewise analyytic function. Hampton, Va: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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4

Orsatti, Paola. Materials for a History of the Persian Narrative Tradition. Venice: Edizioni Ca' Foscari, 2019. http://dx.doi.org/10.30687/978-88-6969-354-0.

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The two essays gathered here, devoted to the characters of Turandot/Būrān-dukht and Farhād respectively, represent two parallel upshots of a stream of research focusing on the transformation of historical or semi-historical figures into literary characters. The research moves from literary characters and their possible historical or legendary origins, to un understanding of their literary function in Persian literature.

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5

Efthimiou, Costas. Spherical harmonics in p dimensions. New Jersey: World Scientific, 2014.

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6

Doye, Eli. Myths from Northeast India: Functional perspective of Galo myths in a changing context. New Delhi: Nation Press, 2018.

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7

Smith, James. Highly accurate beam torsion solutions using the p-Version finite element method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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8

Croally, N. T. Euripidean polemic: The Trojan women and the function of tragedy. Cambridge: Cambridge University Press, 1994.

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9

Kalmar, Tomás Mario. King Alfred the Great, his Hagiographers and his Cult. Nieuwe Prinsengracht 89 1018 VR Amsterdam Nederland: Amsterdam University Press, 2023. http://dx.doi.org/10.5117/9789463729611.

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This book situates Alfred the Great in his hagiographic context. For 150 years, the fables told in the ninth century about Alfred’s childhood have posed interlocking disciplinary challenges to historians committed to evicting romance from history. Blending current Hagiography Studies with historical, literary, and biblical hermeneutics can help us forgo the anti-hagiographic commitments which motivated the scholars who purified the Victorian cult of Alfred by expunging his legends and salvaging his historicity. The book focusses on the typological functions of three Alfredian fables from the Old English Chronicle, the Old English Boethius, and Asser’s Vita Ælfredi, analyses the plot common to all three, critiques the psychological conjecture that Alfred’s childhood memory was their common source, and shows that synoptically they can help us see how Alfred shaped the curve of his own life’s destiny and how he engaged in the formation of his own cult to last a thousand years.

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10

1968-, Arvesú Jorge, and Lopez Lagomasino Guillermo 1948-, eds. Recent advances in orthogonal polynomials, special functions, and their applications: 11th International Symposium on Orthogonal Polynomials, Special Functions, and Their Applications, August 29-September 2, 2011, Universidad Carlos III de Madrid, Leganes, Spain. Providence, R.I: American Mathematical Society, 2012.

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11

Shakespeare and the new disease: The dramatic function of syphilis in Troilus and Cressida, Measure for measure, and Timon of Athens. New York: P. Lang, 1989.

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12

Legendre Polynomials And Functions. CreateSpace Independent Publishing Platform, 2009.

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13

Farrell, Orin J., and Bertram Ross. Solved Problems in Analysis: As Applied to Gamma, Beta, Legendre and Bessel Functions. Dover Publications, Incorporated, 2013.

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14

Solved Problems in Analysis: As Applied to Gamma, Beta, Legendre and Bessel Functions. Dover Publications, Incorporated, 2013.

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15

Mann, Peter. Partial Differentiation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0032.

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This short chapter discusses the Legendre transform, which is used in mechanics to convert between the Lagrangian and the Hamiltonian formulations. The Legendre transform is a mathematical tool that can be used to convert the variables of a function through the methods of partial differentiation in a one-to-one fashion. Developed by Adrien-Marie Legendre in the nineteenth century, it is also central to converting between action principles, generating functions and thermodynamic potentials. By using the Legendre transform, two variables can be expressed in four different ways, via the idea of conjugate pairs; it just depends on what differential quantity is subtracted. Variables that are not considered in the transformation are called passive variables, whiles the important ones are the active variables. The information in this chapter provides the background for many of the other chapters in this book.

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16

Belousov, S. L. Tables of Normalized Associated Legendre Polynomials: Mathematical Tables Series. Elsevier Science & Technology Books, 2014.

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17

Karmazina, L. N., and M. I. Zhurina. Tables of the Legendre Functions P--½+it: Mathematical Tables Series. Elsevier Science & Technology Books, 2016.

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18

Sinha, Amritasu. Applied Differential Equations. Alpha Science International, Limited, 2013.

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19

Chance, Kelly, and Randall V. Martin. Atmospheric Scattering. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199662104.003.0007.

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This chapter describes elastic scattering events, where the wavelength of the scattered light is unchanged from that of the incident light and conservative scattering, scattering without absorption, sometimes closely approximated in clouds. The scattering regime, scattering versus wavelengths and scatterer size are introduced. Polarization in scattering is described by the Stokes vector and the polarization ellipse. Molecular (Rayleigh) scattering is presented and its atmospherically-important inelastic component, Raman scattering (the Ring effect) quantified. Mie scattering for spherical particles is described as is the commonly-used Henyey-Greenstein Mie phase function approximation. Non-spherical scatterers are introduced. The Ångstrom exponent and the expansion of phase functions in Legendre polynomials are described.

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20

Sharif, Shahed, Lisa Berger, Chris Hall, Rachel Pries, and Rene Pannekoek. Explicit Arithmetic of Jacobians of Generalized Legendre Curves over Global Function Fields. American Mathematical Society, 2020.

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21

Mihailova, Tatyana, ed. Mis-, semi- and over communication. Grammar of Unreal-4. LLC MAKS Press, 2020. http://dx.doi.org/10.29003/m1765.978-5-317-06511-9.

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The conference is devoted to the different problems of communication, including misunderstanding and ‘over-understanding'. A special attention is given to the destiny of new personages and images and their function in the legendary tradition. The used data belong to the examples of Medieval Germanic and Celtic narrative tradition, but a modern Scandinavian material is also involved.

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22

Rau, Jochen. Simple Systems. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199595068.003.0004.

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Even though the general framework of statistical mechanics is ultimately targeted at the description of macroscopic systems, it is illustrative to apply it first to some simple systems: a harmonic oscillator, a rotor, and a spin in a magnetic field. These applications serve to illustrate how a key function associated with the Gibbs state, the so-called partition function, is calculated in practice, how the entropy function is obtained via a Legendre transformation, and how such systems behave in the limits of high and low temperatures. After discussing these simple systems, this chapter considers a first example where multiple constituents are assembled into a macroscopic system: a basic model of a paramagnetic salt. It also investigates the size of energy fluctuations and how—in the case of the paramagnet—these fluctuations scale with the number of constituents.

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23

E. S. (Egon Sharpe) 1895-1980 Pearson. Table of the Logarithms of the Complete -Function (for Arguments 2 to 1200, I. E. Beyond Legendre's Range). Creative Media Partners, LLC, 2018.

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24

Mann, Peter. Hamilton’s Principle in Phase Space. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0015.

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This chapter derives Hamilton’s equations using the Legendre transform and the definition of the Hamiltonian function. While, in the Newtonian formalism, conservation laws were rather difficult to tease out, the Lagrangian formalism revolutionised the way of looking at them; however, the Hamiltonian formalism is perhaps even simpler than the Lagrangian formalism, making it straightforward to identify conservation laws and the symmetries of the system associated with each conserved property. In this chapter, the Hamiltonian is treated as being explicitly dependent on time, as this form is more general and will lead to an important relation that, although not an equation of motion, is still useful to discuss. The chapter also introduces Routhian mechanics as a symplectic reduction technique, using integrals of the motion.

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25

Mann, Peter. The Hamiltonian & Phase Space. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0014.

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This chapter discusses the Hamiltonian and phase space. Hamilton’s equations can be derived in several ways; this chapter follows two pathways to arrive at the same result, thus giving insight into the motivation for forming these equations. The importance of deriving the same result in several ways is that it shows that, in physics, there are often several mathematical avenues to go down and that approaching a problem with, say, the calculus of variations can be entirely as valid as using a differential equation approach. The chapter extends the arenas of classical mechanics to include the cotangent bundle momentum phase space in addition to the tangent bundle and configuration manifold, and discusses conjugate momentum. It also introduces the Hamiltonian as the Legendre transform of the Lagrangian and compares it to the Jacobi energy function.

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26

Swendsen, Robert H. An Introduction to Statistical Mechanics and Thermodynamics. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198853237.001.0001.

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This is a textbook on statistical mechanics and thermodynamics. It begins with the molecular nature of matter and the fact that we want to describe systems containing many (1020) particles. The first part of the book derives the entropy of the classical ideal gas using only classical statistical mechanics and Boltzmann’s analysis of multiple systems. The properties of this entropy are then expressed as postulates of thermodynamics in the second part of the book. From these postulates, the structure of thermodynamics is developed. Special features are systematic methods for deriving thermodynamic identities using Jacobians, the use of Legendre transforms as a basis for thermodynamic potentials, the introduction of Massieu functions to investigate negative temperatures, and an analysis of the consequences of the Nernst postulate. The third part of the book introduces the canonical and grand canonical ensembles, which are shown to facilitate calculations for many models. An explanation of irreversible phenomena that is consistent with time-reversal invariance in a closed system is presented. The fourth part of the book is devoted to quantum statistical mechanics, including black-body radiation, the harmonic solid, Bose–Einstein and Fermi–Dirac statistics, and an introduction to band theory, including metals, insulators, and semiconductors. The final chapter gives a brief introduction to the theory of phase transitions. Throughout the book, there is a strong emphasis on computational methods to make abstract concepts more concrete.

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