Evaluation of Some Integrals Following from $L_1$, the Constant of the Asymptotic Expansion of $\ln \Gamma_1 (x+1)$, Originating from Physics (QED)

Abstract

Comparison of three different regularization methods of calculating the one-loop effective Heisenberg-Euler Lagrangian of quantum electro-dynamics (QED) is employed to derive some interesting integrals involving the asymptotic expansion of $\ln \Gamma_1(x+1)$, the generalized $\Gamma$ function. Here it is the constant $L_1$ that will enable us to calculate some integrals which are useful in mathematics as well as in physics.