Lisetska O. New generalizations of Legendre functions and their applications

New generalizations of Legendre functions of the first and second kind are introduced, their main characteristics are studied. Solution of Fredholm integral equation of the first kind with generalized associated Legendre function in kernel is found. Solutions of Volterra integral equations of the first kind containing generalized Legendre functions of the first kind are constructed. Solution of dual integral equations with r-generalized Legendre functions of the first kind in bounded form are found. New generalization of integral transformation of Mehler-Fock type containing generalized Legendre function of the first kind in kernel is constructed and inversion is built.