Generalized product formulas for Whittaker's functions and a novel class of index transforms

Generalized product formulas and index transforms, involving products of Whittaker's functions of different indices are established and investigated. The corresponding inversion formulas are found. Particular cases cover index transforms with products of the modified Bessel and Whittaker's functions. For our goals the Kontorovich-Lebedev and Olevskii transforms of a complex index with nonzero real part are involved.