Geodesic
Euler Integrals and Multi-Integrals of Linear Partial Differential Equations
Matematičeskie zametki, Tome 89 (2011) no. 1, pp. 19-33

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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. 
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     author = {E. I. Ganzha},
     title = {Euler {Integrals} and {Multi-Integrals} of {Linear} {Partial} {Differential} {Equations}},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_1_a2/}
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E. I. Ganzha. Euler Integrals and Multi-Integrals of Linear Partial Differential Equations. Matematičeskie zametki, Tome 89 (2011) no. 1, pp. 19-33. http://geodesic.mathdoc.fr/item/MZM_2011_89_1_a2/