Topics in hypergeometric functions
Keywords:
Gamma function, Euler's reflection formula, Beta function, Hypergeometric series, Binomial sumsSynopsis
This advanced mathematics book addresses the study of selected topics in special functions. The document is structured into three chapters. The rst is dedicated to the Gamma function, presenting the definitions provided by Euler, Gauss, and Weierstrass, and establishing their equivalencies. This first chapter also states and proves some of the most essential properties of the Gamma function, notably the recurrence relation, Euler's reection formula, and Legendre's duplication formula. The second chapter introduces the hypergeometric function, exploring several of its properties. In the third chapter, the developed theory is applied to calculate binomial sums and special series.
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