On integral representations for the zeta-function. (Chinese. English summary) Zbl 1224.11076

Li, Youcheng; Li, Hailong

Pure Appl. Math. 26, No. 3, 409-412 (2010).

Summary: Integral representations for the zeta-function are studied. By using the methods of analytic number theory, we derive Hermite’s formula for the Hurwitz zeta-function from the functional equation for the Riemann zeta-function, and obtain Binet’s second expression for the Gamma function from Hermite’s formula, thus we show the properties of the Gamma function from the zeta-function.

MSC:

11M35	Hurwitz and Lerch zeta functions
33B15	Gamma, beta and polygamma functions

Keywords:

Gamma function; Binet’s formula; Hermite’s formula; Hurwitz zeta-function