Lie group symmetries and Riemann function of Klein–Gordon–Fock equation with central symmetry

•Lie symmetries of Klein–Gordon–Fock equation with central symmetry are found.•New families of exact reference solutions of the equation are obtained.•Riemann function is constructively derived via the symmetries in two ways.

In the present paper Lie symmetry group method is applied to find new exact invariant solutions for Klein–Gordon–Fock equation with central symmetry. The found invariant solutions are important for testing finite-difference computational schemes of various boundary value problems of Klein–Gordon–Fock equation with central symmetry. The classical admitted symmetries of the equation are found. The infinitesimal symmetries of the equation are used to find the Riemann function constructively.