Euler and the Duplication Formula for the Gamma-Function
Alexander Aycock
TL;DR
This paper demonstrates how Euler's formulas for hypergeometric series lead to the derivation of the Gamma-function's duplication formula, providing a historical and mathematical insight into classical analysis.
Contribution
It establishes a connection between Euler's hypergeometric series formulas and the Gamma-function duplication formula, serving as an addendum to previous work.
Findings
Derivation of the Gamma duplication formula from Euler's hypergeometric series formulas
Historical insight into Euler's contributions to special functions
Clarification of the relationship between hypergeometric series and Gamma-function identities
Abstract
We show how the formulas in paper Variae considerationes circa series hypergeometricas written by Euler imply the duplication formula for the Gamma-function. This paper can be seen as an Addendum to a previous paper by the author.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Mathematics and Applications