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A gamma function in two variables
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Mohamed El Bachraoui
Published/Copyright:
February 28, 2014
Abstract
We introduce a gamma function Γ(x, z) in two complex variables which extends the classical gamma function Γ(z) in the sense that lim x→1Γ(x, z) =Γ (z). We will show that many properties which Γ(z) enjoys extend in a natural way to the function Γ(x, z). Among other things we shall provide functional equations, a multiplication formula, and analogues of the Stirling formula with asymptotic estimates as consequences.
Received: 2013-3-22
Accepted: 2014-1-27
Published Online: 2014-2-28
Published in Print: 2014-3-28
©2014 Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Embedding theorems corresponding to correct solvability of a linear differential equation of the first order
- On almost asymptotically lacunary statistical equivalent sequences induced probabilistic norms
- A gamma function in two variables
- Mean value theorems for polyharmonic functions: A conjecture by Picone
- The Euler φ-function associated to automorphic L-functions
- Uniqueness and value-sharing of meromorphic functions with finite weight
- Location of the weighted Fermat–Torricelli point on the K-plane (Part II)
- Optimal estimate on Hausdorff dimension of Reifenberg sets
Keywords for this article
Gamma function;
generalized gamma function;
functional equations;
special functions
Articles in the same Issue
- Frontmatter
- Embedding theorems corresponding to correct solvability of a linear differential equation of the first order
- On almost asymptotically lacunary statistical equivalent sequences induced probabilistic norms
- A gamma function in two variables
- Mean value theorems for polyharmonic functions: A conjecture by Picone
- The Euler φ-function associated to automorphic L-functions
- Uniqueness and value-sharing of meromorphic functions with finite weight
- Location of the weighted Fermat–Torricelli point on the K-plane (Part II)
- Optimal estimate on Hausdorff dimension of Reifenberg sets
