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

2009/03/26 by Donal F. Connon, Connon, Donal F. · 4 citations
Mathematics · #11M06 #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #math.CA #msc:11M06

paper · pdf · doi:10.48550/arxiv.0903.4539

arxiv created 2009/03/26 · openalex publication_date 2009/03/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Some trigonometric integrals involving the log gamma and the digamma function
• The difference between two Stieltjes constants
• Some integrals involving the Stieltjes constants:Part II
• A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations

Related

• Contributions to the Theory of the Barnes Function
• Euler and the Duplication Formula for the Gamma-Function
• Some applications of the Stieltjes constants
• Double series expression for the Stieltjes constants
• On the definition of higher Gamma functions