New proofs of the duplication and multiplication formulae for the gamma and the Barnes double gamma functions

Abstract

New proofs of the duplication formulae for the gamma and the Barnes double gamma functions are derived using the Hurwitz zeta function. Concise derivations of Gauss's multiplication theorem for the gamma function and a corresponding one for the double gamma function are also reported. This paper also refers to some connections with the Stieltjes constants.

References in corpus (2)

• Contributions to the Theory of the Barnes Function
• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I

Cited by in corpus (4)

• Full counting statistics for interacting trapped fermions
• The difference between two Stieltjes constants
• Some trigonometric integrals involving the log gamma and the digamma function
• Some integrals involving the Stieltjes constants:Part II