On some general integral formulae

Year 2024, , 1 - 11, 15.03.2024

Norbert Ortner , Peter Wagner

https://doi.org/10.33205/cma.1406998

Abstract

We repeat and reformulate some more or less known general integral formulae and deduce from them some applications in a concise way. We then present some general double integral formulae which play an essential role in the calculation of fundamental solutions to homogeneous elliptic operators. In particular, this yields generalizations of definite integrals found in standard integral tables. In the final section, the area of an ellipsoidal hypersurface in $\textbf{R}^n$ is represented by a hyperelliptic integral.

Keywords

Leray’s formula, elliptic integrals, definite double integrals

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