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Answer To A Question Concerning Euler's Paper "Variae Considerationes Circa Series Hypergeometricas", Alexander Aycock
Answer To A Question Concerning Euler's Paper "Variae Considerationes Circa Series Hypergeometricas", Alexander Aycock
Euleriana
We solve a problem concerning Euler's paper "Variae considerationes circa series hypergeometricas" (\cite{E661}), as suggested by G. Faber in the preface to Volume 16,2 of the first series of Euler's Opera Omnia. Our solution employs methods introduced by Euler at other places.
Translation Of Euler's Paper E421, Alexander Aycock
Translation Of Euler's Paper E421, Alexander Aycock
Euleriana
This is paper is the result of Euler’s findings on the Eulerian integral of second kind, i.e. the Γ-function: It summarises results and formulas on and properties of the integral in the title that Euler had obtained up to this point in his career and offers more elegant proofs of those before-mentioned results, formulas and properties. The results include a derivation of the integral in the title from an algebraic integral, the reflection formula for the Γ-function and finally a formula equivalent to the Gaußian multiplication formula for the Γ-function, expressed by Euler using mere integrals of algebraic functions.