On one equality of integrals

A. A. Dmitriev

Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok

Abstract: The note proves the equality
$$\frac1{2\pi i}\mskip-8mu\oint_{|z|=r}\mskip-8mu\ln\mskip-4mu\left[1{-}f(z)\left(z{+}\frac1z\right)\right]dz= -\frac1{2\pi i}\mskip-8mu\oint_{|z|=r}\mskip-4mu\exp\left(\frac{1{-}\sqrt{1-4f^2(z)}}{2zf(z)}\right)dz.$$


Key words: integral.

UDC: 517

MSC: 30E20

Received: 30.03.2022

DOI: 10.47910/FEMJ202204

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