MATHEMATICS

Integral representations for the argument of the gamma function of a complex variable

A. B. Kostin^ab, V. B. Sherstyukov<sup>ab

a</sup> Lomonosov Moscow State University
^b Moscow Center for Fundamental and Applied Mathematics

Abstract: New analytical representations of the argument of the gamma function at points of the complex plane have been found. For this value, integral formulas of two types have been obtained. Characteristic examples are analyzed.

Keywords: gamma function, argument of a complex quantity, principal value of an argument, integral representation, Fourier sine transform, Lambert W function, Euler–Maclaurin summation formula.

UDC: 517.581

Presented: I. A. Sokolov
Received: 20.05.2025
Revised: 23.06.2025
Accepted: 23.06.2025

DOI: 10.7868/S3034504925040031

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