Integral equations for special functions of Heun class (Q1359363)

The 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.