Uniform asymptotic expansions of the incomplete gamma functions and the incomplete beta function

1975/01/01 by N. M. Temme · 90 citations
Engineering · Computer Science · Mathematics · #Control Systems and Identification #Target Tracking and Data Fusion in Sensor Networks #Mathematical Analysis and Transform Methods #Mathematics #Incomplete gamma function #Asymptotic expansion #Function (biology) #BETA (programming language) #Series (stratigraphy) #Asymptotic analysis #Gamma function #Beta function (physics) #Error function #Mathematical analysis #Applied mathematics #Algorithm

paper · open access · doi:10.1090/s0025-5718-1975-0387674-2

published in Mathematics of Computation 29(132), 1109-1114 (American Mathematical Society)

openalex publication_date 1975/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

New asymptotic expansions are derived for the incomplete gamma functions and the incomplete beta function. In each case the expansion contains the complementary error function and an asymptotic series. The expansions are uniformly valid with respect to certain domains of the parameters.

Citations

• Asymptotische Eigenschaften der unvollst�ndigen Gammafunktion

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• Incomplete gamma function [wikipedia]