Euler Integrals and Multi-Integrals of Linear Partial Differential Equations

E. I. Ganzha

Krasnoyarsk State Pedagogical University named after V. P. Astaf'ev

Abstract: In this paper, we discuss the notion of reducibility of solutions of the Euler form generalizing solutions arising from the Laplace cascade method for integrating second-order hyperbolic equations in the plane. We present reduction algorithms and prove the equivalence of various possible exact definitions of the reduction of similar explicit solutions.

Keywords: Euler integral and multi-integral, linear partial differential equation, Laplace cascade integration method, reduction algorithm.

UDC: 517.95

Received: 24.03.2009

DOI: 10.4213/mzm8367

 English version: Mathematical Notes, 2011, 89:1, 37–50

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