Discrete Fourier-Jacobi transform.

Discrete analogues of the classical Fourier-Jacobi transform are introduced and investigated. It involves series and integrals with respect to parameters of the Gauss hypergeometric function 2 F 1 (a + i n / 2 , a − i n / 2 ; c ; − x 2) , x > 0 , n ∈ N , a , c > 0 , i is the imaginary unit. The corresponding inversion formulas for suitable functions and sequences in terms of these series and integrals are established. [ABSTRACT FROM AUTHOR]