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This book presents a novel journey of the Gauss hypergeometric function and contains the different versions of the Gaussian hypergeometric function, including its classical version. In particular, the $q$-Gauss or basic Gauss hypergeometric function, Gauss hypergeometric function with matrix arguments, Gauss hypergeometric function with matrix parameters, the matrix-valued Gauss hypergeometric function, the finite field version, the extended Gauss hypergeometric function, the $(p, q)$- Gauss hypergeometric function, the incomplete Gauss hypergeometric function and the discrete analogue of Gauss hypergeometric function. All these forms of the Gauss hypergeometric function and their properties are presented in such a way that the reader can understand the working algorithm and apply the same for other special functions. This book is useful for UG and PG students, researchers and faculty members working in the field of special functions and related areas.

Devised in the 19th century, Gauss and Jacobi Sums are classical formulas that form the basis for contemporary research in many of today's sciences. This book offers readers a solid grounding on the origin of these abstract, general theories. Though the main focus is on Gauss and Jacobi, the book does explore other relevant formulas, including Cauchy.

The influence of Ramanujan on number theory is without parallel in mathematics. His papers, problems and letters have spawned a remarkable number of later results by many different mathematicians. Here, his 37 published papers, most of his first two and last letters to Hardy, the famous 58 problems submitted to the Journal of the Indian Mathematical Society, and the commentary of the original editors (Hardy, Seshu Aiyar and Wilson) are reprinted again, after having been unavailable for some time. In this, the third printing of Ramanujan's collected papers, Bruce Berndt provides an annotated guide to Ramanujan's work and to the mathematics it inspired over the last three-quarters of a century. The historical development of ideas is traced in the commentary and by citations to the copious references. The editor has done the mathematical world a tremendous service that few others would be qualified to do.

This volume presents the idea that one studies orthogonal polynomials and special functions to use them to solve problems.