On the generalized Euler–Stieltjes constants for the Rankin–Selberg L-function

Let [Formula: see text] be a number field of a finite degree and let [Formula: see text] be the Rankin–Selberg [Formula: see text]-function associated to unitary cuspidal automorphic representations [Formula: see text] and [Formula: see text] of [Formula: see text] and [Formula: see text], respectively. The main result of the paper is an asymptotic formula for evaluation of coefficients appearing in the Laurent (Taylor) series expansion of the logarithmic derivative of the function [Formula: see text] at [Formula: see text]. As a corollary, we derive orthogonality and weighted orthogonality relations.