Vistas Of Special Functions II

Description

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. The Theory of Bernoulli and Allied Polynomials The Theory of the Gamma and Related Functions The Theory of the Lipschitz-Lerch Transcendent Elucidation of Zeta-Identities Hypergeometric Functions and Zeta-Functions The Theory of Bessel Functions and the Epstein Zeta-Functions The Theory of Arithmetical Fourier Series and the Parseval Identities Around the Dirichlet L-Functions and the Deninger R-Function