INTEGRATION OF RATIONAL FRACTION AND IDENTICAL RELATIONS OF ELEMENTARY FUNCTIONS OF COMPLEX ARGUMENT
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Abstract
The correctness of the unified approach to integration of rational fractions is justified if there is a product of linear complex conjugate polynomials in the denominator. On its basis, a procedure has been implemented that made it possible to express the real and imaginary parts of the natural logarithm of a complex argument through elementary functions of two variables. This made it possible to prove Euler's formula without using power series theory.
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References
Fikhtengol'ts, G. M. (1968). Osnovy matematicheskogo analiza, t. 1. Moscow: Nauka. (In Russ.).
Shabunin, M. I., & Sidorov, Yu. V. (2016). Teoriya funktsii kompleksnogo peremennogo. Moscow: Laboratoriya znanii. (In Russ.).
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