Die Gammafunktion

Discusses the theory of gamma function. This book covers properties related to the integral representations for $\Gamma(x)$. It explores the properties of functions defined via series of factorials: $\Omega(x)=\sum s\! a_s/(x(x+1)\ldots(x+s))$, with applications to the gamma function.

This title consists of both original volumes of this classic, now published as one. The first volume is a handbook of the theory of the gamma function. The first part of this volume gives an elementary presentation of the fundamental properties of the gamma function (and related functions) as applications of the theory of analytic functions. The second part covers properties related to the integral representations for $\Gamma(x)$. The third part explores the properties of functions defined via series of factorials: $\Omega(x)=\sum s! a s/(x(x+1)\ldots(x+s))$, with applications to the gamma function. The Handbook is an often-cited reference in the literature on the gamma function and other transcendental functions. The second (and shorter) volume covers the theory of the logarithmic integral $\textnormal{li (x)$ and certain related functions. Specific topics include integral representations, asymptotic series, and continued fractions.