An Introduction to Hypergeometric Functions

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.

- 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.