Vistas of special functions

著者

• 金光, 滋 カネミツ, シゲル
• 塚田, 春雄 ツカダ, ハルオ
• Chakraborty, Kalyan

書誌事項

Vistas of special functions

Shigeru Kanemitsu & Haruo Tsukada

World Scientific Pub., c2007-c2010

• [1]
• 2

注記

[1]: Includes bibliographical references (p. 207-211) and index

2: Includes bibliographical reference (p. 259-269) and index

2: Other author: Kalyan Chakraborty

内容説明・目次

巻冊次

[1] ISBN 9789812707741

内容説明

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.

目次

• Bernoulli Polynomials
• The Gamma Function
• The Hurwitz Zeta-Function
• Bernoulli Polynomials via the Hurwitz Zeta-Function
• The Gamma Function via the Hurwitz Zeta-Function
• Bessel Functions and Crystal Symmetry
• Fourier Series and Fourier Transforms
• Finite Fourier Series.

巻冊次

2 ISBN 9789814273978

内容説明

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.

目次

• Bernoulli and Allied Polynomials
• Chebyshev Polynomials and Energy Levels of Carbon Hydrates
• The Gamma Function Continued - Kummer's Fourier Series, The Stirling Formulas, Etc.
• The Hurwitz-Lerch Zeta-Function
• The Dirichlet L-Function
• Arithmetical Fourier Series
• The Madelung Constants and Special Functions
• Applications of Fourier Series - Parseval Identity
• The Derivative of Dirichlet L-Function and the Kronecker Limit Formula.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA83015574
• ISBN:
  • 9789812707741
  • 9789814273978
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: New Jersey
• ページ数/冊数: 2 v.
• 大きさ: 24 cm