Integral representations for the Gamma function, the Beta function, and the Double Gamma function

DOI10.1080/10652460902943519zbMath1242.33002OpenAlexW1991884917MaRDI QIDQ3651168

Junesang Choi, Hari M. Srivastava

Publication date: 8 December 2009

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460902943519

zbMATH Keywords

beta functiongamma functionpsi (or digamma) functiondouble gamma functionGlaisher-Kinkelin constantEuler-Mascheroni constantRiemann's zeta functiondeterminants of the LaplaciansHurwitz-Lerch zeta functionWeierstrass factorization theoremHurwitz' (or generalized) zeta functionWeierstrass' canonical product

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Classical hypergeometric functions, ({}_2F_1) (33C05) Hurwitz and Lerch zeta functions (11M35) Evaluation of number-theoretic constants (11Y60)

Related Items (9)

Multiple Gamma Functions and Their Applications ⋮ Asymptotic formulas for the triple gamma function \(\varGamma _{3}\) by means of its integral representation ⋮ More asymptotic expansions for the Barnes \(G\)-function ⋮ A class of two-sided inequalities involving the psi and polygamma functions ⋮ Integral Representations for the Euler-Mascheroni Constant γ ⋮ Some uniqueness results for the non-trivially complete monotonicity of a class of functions involving the polygamma and related functions ⋮ Approximations for the ratio of the gamma functions via the digamma function and its applications ⋮ Some inequalities and monotonicity properties associated with the gamma and psi functions and the BarnesG-function ⋮ Sufficient conditions for strongly star-like functions involving the generalized Srivastava–Attiya operator

Cites Work

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• Spectral functions, special functions and the Selberg zeta function
• Extremals of determinants of Laplacians
• Zeta regularized products and functional determinants on spheres
• Some relationships between the generalized Apostol–Bernoulli polynomials and Hurwitz–Lerch Zeta functions
• Some expansion formulas for a class of generalized Hurwitz–Lerch Zeta functions
• Determinants of Laplacians and Multiple Gamma Functions
• A certain class of series associated with the zeta function
• THE FIRST EULERIAN INTEGRAL
• A generalization of the Hurwitz - Lerch Zeta function

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