On the evaluation of the function phi(lambda)=1/2-pi-i-integral-sigma+i-infinity/sigma-i-infinity-eunin(+)-lambda-udu for real values of lambda

Abstract

The evaluation of the function mentioned in the t itle is done by deriving a y mptotic formulas with error terms for the large values of 1 A I. For values of A in the remainin g finite interval, Simpson's rule is applied after suitable transformation of the path of integrat ion and restriction to a finite portion of this path. A table of the function is given together with guesses of the errors due to the discretization and the fini te integration limits. 1. 6524E-01 -3.