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Vistas of special functions II /
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
2007.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; Contents; 1. The theory of Bernoulli and allied polynomials; 2. The theory of the gamma and related functions; 2.1 Gamma function; 2.2 The Euler digamma function; 3. The theory of the Hurwitz-Lerch zeta-functions; 3.1 Introduction; 3.2 Integral representations; 3.3 A formula of Ramanujan; 3.4 Some definite integrals; 3.5 The functional equation; 4. The theory of Bernoulli polynomilas via zeta-functions; 5. The theory of the gamma and related functions via zeta-functions; 5.1 Derivatives of the Hurwitz zeta-function.
- 5.2 Asymptotic formulas for the Hurwitz and related zetafunctions in the second variable5.3 An application of the Euler digamma function; 5.4 The first circle; 6. The theory of Bessel functions and the Epstein zeta-functions; 6.1 Introduction and the theory of Bessel functions; 6.2 The theory of Epstein zeta-functions; 6.3 Lattice zeta-functions; 6.4 Bessel series expansions for Epstein zeta-functions; 7. Fourier series and Fourier transforms; 7.1 Fourier series; 7.2 Integral transforms; 7.3 Fourier transform; 7.4 Mellin transform; 8. Around Dirichlet's L-functions.
- 8.1 The theory of periodic Dirichlet series8.2 The Dirichlet class number formula; 8.3 Proof of the theorems; Appendix A Complex functions; A.1 Function series; A.2 Residue theorem and its applications; Appendix B Summation formulas and convergence theorems; B.1 Summation formula and its applications; B.2 Application to the Riemann zeta-function; Bibliography; Index.