A curious formula related to the Euler Gamma function
Farhi, Bakir
Original · EN
In this note, we prove that for all x ∈ (0, 1), we have: Γ(x) = 1/2 π+ πη (1/2 - x) - 1/2 (πx) + 1π ∑ₙ ₌ ₁∞ n/n (2 πn x), where Γ denotes the Euler Gamma function and η:= 2 ∫₀¹ Γ(x) · (2 πx) d x = 0.7687478924
English translation
This paper has no Arabic translation yet. Be the first: it takes a few seconds, and the result is stored for every future reader.