Journal of Mathematical Sciences

, Volume 130, Issue 5, pp 4911–4940 | Cite as

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

  • A. V. Aksenov


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.


General Solution Bessel Function Recursive Relation Differential Relation 
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© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. V. Aksenov
    • 1
  1. 1.Moscow State UniversityMoscowRussia

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