The Gamma Function
The Gamma Function is the finest book dedicated to the topic of the Gamma function. It is concise and thorough, covering the most important aspects of Gamma. Written in an easily understandable manner, the book is well-suited for advanced undergraduates in science and mathematics.
The Gamma function has important applications in probability theory, combinatorics and most, if not all, areas of physics. A large number of proofs and derivations of theorems and identities are covered in the book including: Analytic continuation of the factorials, properties via complex analysis, convexity and the Gamma function, the Beta function, Wallis’s integrals, Wallis’s product, product & reflection formulas, half-integer values, digamma and polygamma functions, series expansions, Euler-Mascheroni integrals, duplication & multiplication formulas, the Gamma and zeta function relationships, Hankel’s contour integral representation, Stirling’s formula, the Weierstrass factor theorem and the Mittag-Leffler theorem.