Vistas Of Special Functions
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Vistas Of Special Functions
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Author : Shigeru Kanemitsu
language : en
Publisher: World Scientific
Release Date : 2007-06-07
Vistas Of Special Functions written by Shigeru Kanemitsu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-07 with Mathematics categories.
This is a unique book for studying special functions through zeta-functions. Many important formulas of special functions scattered throughout the literature are located in their proper positions and readers get enlightened access to them in this book. The areas covered include: Bernoulli polynomials, the gamma function (the beta and the digamma function), the zeta-functions (the Hurwitz, the Lerch, and the Epstein zeta-function), Bessel functions, an introduction to Fourier analysis, finite Fourier series, Dirichlet L-functions, the rudiments of complex functions and summation formulas. The Fourier series for the (first) periodic Bernoulli polynomial is effectively used, familiarizing the reader with the relationship between special functions and zeta-functions.
Vistas Of Special Functions
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Author : Shigeru Kanemitsu
language : en
Publisher: World Scientific
Release Date : 2007
Vistas Of Special Functions written by Shigeru Kanemitsu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
1. The theory of Bernoulli and allied polynomials -- 2. The theory of the gamma and related functions -- 3. The theory of the Hurwitz-Lerch zeta-functions -- 4. The theory of Bernoulli polynomials via zeta functions -- 5. The theory of the gamma and related functions via zeta-functions -- 6. The theory of Bessel functions and the Epstein zeta-functions -- 7. Fourier series and Fourier transforms -- 8. Around Dirichlet's L-functions.
Vistas Of Special Functions Ii
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Author : Haruo Tsukada
language : en
Publisher: World Scientific
Release Date : 2009-10-28
Vistas Of Special Functions Ii written by Haruo Tsukada and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-28 with Mathematics categories.
This book (Vista II), is a sequel to Vistas of Special Functions (World Scientific, 2007), in which the authors made a unification of several formulas scattered around the relevant literature under the guiding principle of viewing them as manifestations of the functional equations of associated zeta-functions. In Vista II, which maintains the spirit of the theory of special functions through zeta-functions, the authors base their theory on a theorem which gives some arithmetical Fourier series as intermediate modular relations — avatars of the functional equations. Vista II gives an organic and elucidating presentation of the situations where special functions can be effectively used. Vista II will provide the reader ample opportunity to find suitable formulas and the means to apply them to practical problems for actual research. It can even be used during tutorials for paper writing.
Special Functions
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Author : George E. Andrews
language : en
Publisher: Cambridge University Press
Release Date : 1999
Special Functions written by George E. Andrews and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
Special Functions
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Author : Zhi Xu Wang
language : en
Publisher: World Scientific
Release Date : 1989-10-01
Special Functions written by Zhi Xu Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-10-01 with Mathematics categories.
In this book, expansions of functions in infinite series and infinite product and the asymptotic expansion of functions are discussed. This may be the best reference book on Special Functions.
Completeness And Basis Properties Of Sets Of Special Functions
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Author : J. R. Higgins
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-03
Completeness And Basis Properties Of Sets Of Special Functions written by J. R. Higgins and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-03 with Mathematics categories.
Presents methods for testing sets of special functions for completeness and basis properties, mostly in L2 and L2 spaces.
Special Functions
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Author : Richard Beals
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-12
Special Functions written by Richard Beals and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-12 with Mathematics categories.
The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.
Encyclopedia Of Special Functions The Askey Bateman Project
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Author : Mourad E. H. Ismail
language : en
Publisher: Cambridge University Press
Release Date : 2020-09-17
Encyclopedia Of Special Functions The Askey Bateman Project written by Mourad E. H. Ismail and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-17 with Mathematics categories.
Extensive update of the Bateman Manuscript Project. Volume 1 covers orthogonal polynomials and moment problems.
Lectures On Orthogonal Polynomials And Special Functions
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Author : Howard S. Cohl
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-15
Lectures On Orthogonal Polynomials And Special Functions written by Howard S. Cohl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-15 with Mathematics categories.
Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.
The Lerch Zeta Function
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Author : Antanas Laurincikas
language : en
Publisher: Springer Science & Business Media
Release Date : 2002
The Lerch Zeta Function written by Antanas Laurincikas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This monograph is a generalization of the classic Riemann, and Hurwitz zeta-functions, containing both analytic and probability theory of Lerch zeta-functions.