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Linear Differential Relations Between Solutions of the Class of Euler-Poisson-Darboux Equations

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Abstract

All the linear first-order relations of the form

$$u^{(\beta )} = A(r,z)\frac{{\partial u^{(\alpha )} }}{{\partial r}} + B(r,z)\frac{{\partial u^{(\alpha )} }}{{\partial z}} + C(r,z)u^{(\alpha )}$$

between solutions u = u (α) and u = u (β) of the class of Euler-Poisson-Darboux (EPD) equations are obtained. We consider applications of the obtained relations for obtaining identities between the EPD operators, recursive relations for the Bessel function, and general solutions of the EPD equation in special cases in application to the gas dynamics of a polytropic gas.

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  1. Moscow State University, Moscow, Russia

    A. V. Aksenov

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 12, Partial Differential Equations, 2004.

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Aksenov, A.V. Linear Differential Relations Between Solutions of the Class of Euler-Poisson-Darboux Equations. J Math Sci 130, 4911–4940 (2005). https://doi.org/10.1007/s10958-005-0390-x

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