One group of hybrid integral transforms of the type Legendre 2nd kind--Fourier--\dots--Legendre--Fourier on polar axis (Q2753486)

The following singular Stourm-Liouville problem on the real axis is considered: to construct in \(0<R_0\leq r<\infty\) a solution of a separable system of ordinary differential equations satisfied by trigonometric functions in intervals with even numbers and by the Legendre functions in intervals with odd numbers (the last \((2n+1)\)th interval is infinite) under some conjugation conditions at \(2n\) conjugation points. Using the technique of delta-like sequences (Dirichlet kernel), a hybrid integral transform of the Legendre 2nd kind--Fourier--\dots--Legendre--Fourier type is derived. The main identity of integral transform of a hybrid differential operator is obtained.