An Introduction to Hypergeometric Functions
Description
This textbook provides an elementary introduction to hypergeometric functions, which generalize the usual elementary functions. It includes plenty of solved exercises and it is appropriate for a wide audience, starting from undergraduate students in mathematics, physics and engineering. Since the presented functions are limited to hypergeometric functions of a real variable, the only prerequisites are the basics of real analysis.
Reviews / Votes
"This textbook is a valuable resource for students and researchers looking to grasp the theory and applications of hypergeometric series, offering both deep theoretical insights and practical tools for further exploration in the field." (Roberto S. Costas-Santos, zbMATH 1558.33001, 2025)
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Person
Daniel Duverney . Born in 1955, Dr. Duverney has taught in highschools and in higher schools for engineering and science preparatory classes. He got his PhD and Habilitation Thesis in the University of Lille. He has written more than 40 research papers (alone or in collaboration with Japanese mathematicians). He has also written three books in French: The first one is an introduction to Number Theory (also translated into Japanese and English), the second (written in collaboration with four colleagues) deals with the mathematical curriculum of the first year of the preparatory classes, and the third book consists in an elementary presentation of hypergeometric functions. All three books include a great number of solved exercises.
Content
- 1. Eulerian Functions.- 2. Polygamma Functions.- 3. Hypergeometric Functions.- 4. Gauss Hypergeometric Function.- 5. Elliptic Integrals.- 6. Kummer Hypergeometric Function.- 7. Bessel Functions.- 8. Polylogarithm Function.- 9. Classical Orthogonal Polynomials.- 10. q-Hypergeometric Functions.