This book presents various integral expansions related to the Mehler-Fock and Mehler-Fock type transforms involving spherical harmonics, namely, Legendre, associated Legendre, generalized associated Legendre, non-periodic Legendre and associated Legendre functions.

An important class of integral expansions generated by Sturm-Liouville theory involving spherical harmonics is commonly known as Mehler-Fock integral transforms. In this book, a number of integral expansions of such type have been established rigorously. As applications, integral expansions of some simple function are also obtained.