Integral equations for special functions of Heun class.

*(English)*Zbl 0883.34029The authors study integral equations equivalent to boundary problems for the differential equations with regular singular points. A new method of their derivation is proposed which is not as general as the known ones but is efficient in creating integral equations of a certain type.

A number of new integral equations are obtained, some related to the double-confluent Heun equation. Formal calculations at the first stage are followed by several rigorous theorems based on the asymptotic behavior at singularities, and on convergence of integrals depending on a parameter.

Reviewer: R.S.Dahiya (Ames)

##### MSC:

34B30 | Special ODE (Mathieu, Hill, Bessel, etc.) |

33C99 | Hypergeometric functions |

34A25 | Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.) |