Series representations of the Volterra function and the Fransén-Robinson constant
type: Item
instance of: scholarly article
title: Series representations of the Volterra function and the Fransén-Robinson constant
zbMATH Open document ID: 1499.33087
author: Pedro J. Pagola
author: Pablo Palacios
author: José L. López
published in: Journal of Approximation Theory
publication date: 2021-12-01T00:00:00Z
review text: This paper discusses the Volterra function \(\mu(t,\beta,\alpha)\), and presents several convergent expansions of this function in terms of incomplete gamma functions. These expansions may be used to implement numerical evaluation techniques for this function. As an application the paper contains a numerical series representation of the Fransén-Robinson constant. Some numerical examples demonstrate the accuracy of approximation. The paper is organized as follow: some preliminary results needed for the analysis are introduced, given is an integral representation of the Volterra function which is different from the original definition. The expansion of the function by incomplete gamma functions is defined. The main result is derived, which is a family of convergent series representation of the Volterra function. The numerical series representation of the Fransén-Robinson constant and numerical experiments that show the accuracy of the expansion follow. Proofs are given throughout the sections, for the stated theorems and claimed results. The paper ends with acknowledgments and 15 references.
Mathematics Subject Classification ID: 33E20
Mathematics Subject Classification ID: 41A58
zbMATH DE Number: 7436511
zbMATH Keywords: Volterra function
zbMATH Keywords: Fransén-Robinson constant
zbMATH Keywords: convergent series representation
zbMATH Keywords: special functions
MaRDI profile type: Publication
full work available at URL: j.jat.2021.105641
OpenAlex ID: W3194475341
cites work: Q3579593
cites work: Q5849055
cites work: Q5847356
cites work: Calculation of the Moments and the Moment Generating Function for the Reciprocal Gamma Distribution
cites work: On Volterra functions and Ramanujan integrals
cites work: The Two Forms of Fractional Relaxation of Distributed Order
cites work: Time-fractional Diffusion of Distributed Order
cites work: The Asymptotic behaviour Of μ(z, β, α)
DOI: 10.1016/J.JAT.2021.105641
Recommended article: Some Integrals of Gamma, Polygamma and Volterra Functions
Recommended article: On Volterra functions and Ramanujan integrals
Recommended article: Q3718070
Recommended article: Computation of the incomplete gamma function ratios and their inverse
Recommended article: Q4764057
Recommended article: Q2960866
Recommended article: An asymptotic expansion for the incomplete beta function
Recommended article: Continued fraction approximation and inequality of the gamma function
Recommended article: The asymptotic series of the generalized Stirling formula
Recommended article: Expansions of the exponential integral in incomplete gamma functions
describes a project that uses: Digital Library of Mathematical Functions
description: scientific article; zbMATH DE number 7436511