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.
Asymptotic Expansion of the Heat Kernel Trace of Laplacians with Polynomial Potentials
Fine structure of the asymptotic expansion of cyclic integrals
Asymptotic Expansion of the Eigenvalues of a Bathtub Potential with Quadratic Ends
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