In the first quadrant of the complex plane, a new representation of the countable-valued function Arg (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 (z) (-, ] 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.
Kostin et al. (Mon,) studied this question.