On Buschman–Erdelyi and Mehler–Fock transforms related to the group $SO_0(3,1)$

By using a functional defined on a pair of the assorted represention spaces of the connected subgroup of the proper Lorentz group, a formula for the Buschman–Erdelyi transform of the Legendre function (up to a factor) is derived. Also a formula for the Mehler–Fock transform of the Legendre function of an inverse argument is obtained. Moreover, a generalization of one known formula for the Mehler–Fock transform is derived.