Chapter 1 introduces elementary classical special functions. Gamma, beta, psi, zeta functions, hypergeometric functions and the associated special functions, generalizations to Meijer's G and Fox's H-functions are examined here. Discussion is confined to basic properties and selected applications. Introductionto statistical distribution theory is provided. Some recent extensions of Dirichlet integrals and Dirichlet densities are discussed. A glimpse into multivariable special functions such as Appell's functions and Lauricella functions is part of Chapter 1. Special functions as solutions of differential equations are examined. Chapter 2 is devoted to fractional calculus. Fractional integrals and fractional derivatives are discussed. Their applications to reaction-diffusion problems in physics, input-output analysis, and Mittag-Leffler stochastic processes are developed. Chapter 3 deals with q-hyper-geometric or basic hypergeometric functions. Provides the required mathematical tools for researchers active in the physical sciences. Presents a full suit of elementary functions for scholars at PhD level text and exercises have been class-tested over 5 different years INDICE: Basic Ideas of Special Functions and Statistical Distributions. Mittag-Leffler Functions and Fractional Calculus. An Introduction to q-Series. Ramanujan's Theories of Theta and Elliptic Functions. Lie Group and Special Functions. Applications to Density Estimation. - Applications to Order Statistics. Applications to Astrophysics Problems. An Introduction to Wavelet Analysis. Jacobians of Matrix Transformations. Special Functions of Matrix Argument.
- ISBN: 978-0-387-75893-0
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 400
- Fecha Publicación: 01/03/2008
- Nº Volúmenes: 1
- Idioma: Inglés