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Let E be Galois extension of Q of finite degree and let π and π\u27 be two irreducible automorphic unitary cuspidal representations of GLm(EA) and GLm\u27(EA), respectively. We prove an asymptotic formula for computation of coefficients γπ,π\u27(k) in the Laurent (Taylor) series expansion around s=1 of the logarithmic derivative of the Rankin-Selberg L-function L(s, π × π\u27) under assumption that at least one of representations π, π\u27 is self-contragredient and show that coefficients γπ,π\u27(k) are related to weighted Selberg orthogonality. We also replace the assumption that at least one of representations π and π\u27 is self-contragredient by a weaker one

Euler-Stieltjes constants for the Rankin-Selberg L-function and weighted Selberg orthogonality