An Infinite Product Identity (Open)

Summary: Prove the infinite product identity \prod_{k=1}^{\infty} \frac{(1 + n/k)^{2k+n}}{e^{2n}} = \frac{e^{n^2 + n}}{(2 \pi)^n} \prod_{k=1}^n k^{n-2k}, \quad n = 1,2,3,\ldots.

Classification: Primary, Classical Analysis; Secondary, Sequences and Series

Carlo Sanna
Department of Mathematics
Universita degli Studi di Torino
Turin, Italy
Email: carlo.sanna.dev@gmail.com

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