Properties of Ultra Gamma Function

2017/04/15 by Kuldeep Singh Gehlot, Gehlot, Kuldeep Singh
Mathematics · #33B15 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1704.08189

openalex publication_date 2017/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the integral of type _δ,aΓ_ρ,b(x) =Γ(δ,a;ρ,b)(x)=∫₀^∞t^x-1e^-(t^δ)/(a)-\fract^-ρbdt. Different authors called this integral by different names like ultra gamma function, generalized gamma function, Kratzel integral, inverse Gaussian integral, reaction-rate probability integral, Bessel integral etc. We prove several identities and recurrence relation of above said integral, we called this integral as Four Parameter Gamma Function. Also we evaluate relation between Four Parameter Gamma Function, p-k Gamma Function and Classical Gamma Function. With some conditions we can evaluate Four Parameter Gamma Function in term of Hypergeometric function.

Citations

• Two Parameter Gamma Function and its Properties

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