A.M. Mathai, H.J. Haubold0387758933, 9780387758930
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. Introduction to 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. Chapter 4 covers basic hypergeometric functions and Ramanujan’s work on elliptic and theta functions. Chapter 5 examines the topic of special functions and Lie groups. Chapters 6 to 9 are devoted to applications of special functions. Applications to stochastic processes, geometric infinite divisibility of random variables, Mittag-Leffler processes, alpha-Laplace processes, density estimation, order statistics and astrophysics problems, are dealt with in Chapters 6 to 9. Chapter 10 is devoted to wavelet analysis. An introduction to wavelet analysis is given. Chapter 11 deals with the Jacobians of matrix transformations. Various types of matrix transformations and the associated Jacobians are provided. Chapter 12 is devoted to the discussion of functions of matrix argument in the real case. Functions of matrix argument and the pathway models along with their applications are discussed. |
Table of contents :
Front Matter(pp.i-xxv)……Page 1
Basic Ideas of Special Functions and Statistical Distributions(pp.1-78)……Page 23
Mittag-Leffler Functions and Fractional Calculus(pp.79-134)……Page 101
An Introduction to q-Series(pp.135-157)……Page 157
Ramanujan’s Theories of Theta and Elliptic Functions(pp.159-209)……Page 180
Lie Group and Special Functions(pp.211-245)……Page 231
Applications to Stochastic Process and Time Series(pp.247-295)……Page 266
Applications to Density Estimation(pp.297-309)……Page 315
Applications to Order Statistics(pp.311-340)……Page 328
Applications to Astrophysics Problems(pp.341-387)……Page 358
An Introduction to Wavelet Analysis(pp.389-408)……Page 405
Jacobians of Matrix Transformations(pp.409-428)……Page 425
Special Functions of Matrix Argument(pp.429-455)……Page 445
Back Matter(pp.457-464)……Page 472 |
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