Abel's limit theorem, its converse, and multiplication formulae for Γ(x)
Irish Mathematical Society
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.
Corrected converse , J. E. Littlewood , General identity , Gamma function. , Abel's limit theorem for power series , Gauss's multiplication theorem
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)
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