Far Eastern Mathematical Journal

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On one equality of integrals

Dmitriev A. A.

2022, issue 1, P. 51-54 DOI: https://doi.org/10.47910/FEMJ202204

Abstract

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

Keywords: integral

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References

[1] A. P. Prudnikov, Iu. A. Brychkov, O. I. Marichev, Integraly i riady. T. 1: Elementarnye funktsii, FIZMATLIT, M., 2002, 632 s. [2] G. N. Vatson, Teoriia besselevykh funktsii, IIL, M., 1949, 799 s.

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