The generalized gamma functions

2011/05/30 by Tran Gia Loc, Loc, Tran Gia, Trinh Duc Tai +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1105.6002

openalex publication_date 2011/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a way to generalize the Euler's gamma function as well as some related special functions. With a given polynomial in one variable f(t)≥ 0, we can associate a function, so-called "gamma function associated with f", defined by Γ_f(s) := ∫₀^∞ f^s-1 e^-t dt. This function has many features similar to the Euler's gamma function. We also present some initial results on the gamma-type functional equation for Γ_f(s) in some special cases.

Related

• Euler and the Gammafunction
• Topics in Special Functions
• Notes on the historical bibliography of the gamma function
• Two-dimensional generalized gamma function and its applications
• Properties of Ultra Gamma Function