Representation of a family of functional series by the method of finite integral transform of Lebedev type (Q2753526)

Differential equation \([r^2\,d^2/dr^2 + r(2\alpha+1)d/dr - \lambda^2 r^2 +\alpha^2 -q^2] u(r) = -f(r)\) under some boundary conditions is considered in interval \(R_0 \leq r \leq R\) (\(R_0>0\), \(R<\infty\)). By comparison of solutions, constructed using (i) the technique of fundamental solutions and (ii) the finite integral transform of Lebedev type, a representation of an algebraical family of functional series in modified Bessel functions with imaginary index is obtained.