  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.
