Answers are grounded in this paper and cite their sources.
Analysis of a new formula for gamma function arguments in complex numbers, suggesting applications in differential equations.
In the first quadrant of the complex plane, a new representation of the countable-valued function ArgΓ(z) containing an improper integral of a special form is found. A formula for the principal argument is also discussed. This result, together with known properties of the gamma function, makes it possible to evaluate Γ(z)∈(-π,π] at points z of the other quadrants. Illustrative examples are analyzed. The obtained relations may be useful, e.g., in solving problems related to asymptotics of solutions to nonlinear differential equations of mathematical physics.
No takes yet. Share an insight, caveat, or question.
Kostin et al. (2025) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: