2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228752Using an integral of a hypergeometric function, we give necessary and sufficient conditions for irrationality of Euler's constant $γ$. The proof is by reduction to known irrationality criteria for $γ$ involving a Beukers-type double integral. We show that the hypergeometric and double integrals are equal by evaluating them. To do this, we introduce a construction of linear forms in 1, $γ$, and logarithms from Nesterenko-type series of rational functions. In the Appendix, Sergey Zlobin gives a change-of-variables proof that the series and the double integral are equal.Typos in statement of Lemma 2 corrected, reference [3] updated, published version. Appendix by Sergey ZlobinNumber TheoryClassical Analysis and ODEs11J72 (Primary) 11J86, 33C20 (Secondary)text