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

Author： Aksenov A.

Publisher： Springer Publishing Company

ISSN： 1072-3374

Source： Journal of Mathematical Sciences, Vol.130, Iss.5, 2005-11, pp. : 4911-4940

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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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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