Duverney D. An Introduction to Hypergeometric Functions 2024

Textbook in PDF format

This book is suitable to be studied already at the end of the second year of undergraduate studies in mathematics, physics, and engineering. It provides an elementary introduction to hypergeometric functions, which generalize the usual elementary functions. Since the presented functions are limited to hypergeometric functions of a real variable, the only prerequisites are the bases of real analysis: differential and integral calculus, sequences and series of real numbers, power series, ordinary differential equations.
Preface.
Eulerian Functions.
Polygamma Functions.
Hypergeometric Functions.
Gauss Hypergeometric Function.
Elliptic Integrals.
Kummer Hypergeometric Function.
Bessel Functions.
Polylogarithm Function.
Classical Orthogonal Polynomials.
q-Hypergeometric Functions.
Lerch Zeta Function.
Real Analytic Functions.
Inverse Hyperbolic Functions.
Stationary Phase Method.
References.
Index