Binet's second formula, Hermite's generalization, and two related identities
Binet's second formula, Hermite's generalization, and two related identities
Abstract Legendre was the first to evaluate two well-known integrals involving sines and exponentials. One of these integrals can be used to prove Binet’s second formula for the logarithm of the gamma function. Here, we show that the other integral leads to a specific case of Hermite’s generalization of Binet’s …