Discrete Lebedev's index transforms (Q2243675)

The author introduces discrete analogs of the Lebedev transforms with the product of the modified Bessel functions given by the Eqs.~(1.2), (1.3). The author investigates four transformations given by Eq.~(1.4) to Eq. (1.7) employing the theory of the discrete Kontorovich-Lebedev transform recently developed by the author [Ramanujan J. 55, No.~2, 517--538 (2021; Zbl 1476.44005)]. The author provides proofs for the inversion formulas for the expressions presented in Eq.~(1.4) and Eq.~(1.5) in Theorem~1 and Theorem~2, respectively. Finally, he gives the proofs of the inversion theorems (Theorem~3 and Theorem~4) for the discrete transforms presented in Eq.~(1.6) and Eq.~(1.7), respectively.