Contributions to theory of zeta-functions. The modular relation supremacy (Q2842211)

This book provides interesting material on zeta-functions, modular relations, special functions and much else besides. It is said that this is the first volume of the planned trilogy on the contributions to the theory of zeta-functions. The chapters are as follows:NEWLINENEWLINE1. PreludeNEWLINENEWLINE2. Grocery of special functionsNEWLINENEWLINE3. Unprocessed modular relationsNEWLINENEWLINE4. Fourier-Bessel expansion \(H_{1,1}^{1,1} \leftrightarrow H_{0,2}^{2,0}\)NEWLINENEWLINE5. The Ewald expansion or the incomplete Gamma seriesNEWLINENEWLINE6. The Riesz sumsNEWLINENEWLINE7. The general modular relationNEWLINENEWLINE8. The Hecke type zeta-functionsNEWLINENEWLINE9. The product of zeta-functionsNEWLINENEWLINE10. MiscellanyNEWLINENEWLINEThe authors' basic philosophy is to take zeta-symmetry -- the functional equation -- as their guiding principle and try to make up ``a chart of the sea of zeta-functions for the coming young navigators to continue the tradition''. Besides meeting various zeta-functions, the reader will be introduced to many special functions: (generalized) Bessel functions, (generalized) hypergeometric functions, Fox \(H\)-functions, Meijer functions, \(G\)-functions of two variables, etc. This original work contains much non-standard material and will be certainly of interest to many readers.