Description
Book SynopsisThis 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.
Table of ContentsBernoulli 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.
