Abel's limit theorem, its converse, and multiplication formulae for Γ(x)

Holland, Finbarr

Abel's limit theorem, its converse, and multiplication formulae for Γ(x)

Files

Holland-wef_(1).pdf(110.66 KB)

Published Version

Date

2022

Authors

Holland, Finbarr

Publisher

Irish Mathematical Society

Abstract

Abel's well-known limit theorem for power series, and its corrected converse due to J. E. Littlewood, form the basis for a general identity that is presented here, which is shown to be equivalent to Gauss's multiplication theorem for the Gamma function.

Keywords

Corrected converse , J. E. Littlewood , General identity , Gamma function. , Abel's limit theorem for power series , Gauss's multiplication theorem

Citation

Holland, F. (2022) 'Abel's limit theorem, its converse, and multiplication formulae for Γ(x)', Bulletin of the Irish Mathematical Society, 89, pp. 57-64. Available at: https://www.maths.tcd.ie/pub/ims/bull89/wef/Classroom/Holland/Holland-wef.pdf (Accessed: 13 July 2022)