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