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Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included. Other topics include q-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This clearly expressed and readable work can serve as a learning tool and lasting reference for students and researchers in special functions, mathematical physics, differential equations, mathematical computing, number theory, and combinatorics.

Functions, Special. --- Special functions --- Mathematical analysis --- Functions, Special --- Fonctions spéciales --- Hypergeometric functions. --- Hypergeometric series.

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This book discusses a broad range of vital issues in public health, encompassing health facilities, the healthcare system, disease and epidemiological transition of disease, spatio-temporal change of health facilities, disease patterns, and the complex reciprocal relationship between human health and the environment. The book is arranged into three broad sections. Part I: Socio-demographic determinants of public health and policies; Part II: Spatio-temporal & environmental determinants of public health and policies; and Part III: Disease epidemics and challenges. Considering all these overarching themes, this book has been prepared to discuss and provide insights to generate awareness of the holistic perspective of social, cultural, and political factors for public health, disease, epidemics, health facilities, the healthcare system, government policies, prosperity and backdrops in global and local contexts as a geographical perspective. The book should attract the attention of students, researchers, academicians, policymakers and other inquisitive readers interested in different aspects of public health, health geography, and spatial demography.

Geography. --- Public health. --- Demography. --- Public Health. --- Spatial Demography.