Let a > 0, β > -1. The (C t , a, β) transformation of the sequence {s k } is defined by _ Γ(β+n+2)Γ(a-\-β+l) ^ Γ(a + k)Γ(k + n + ϊ) n Γ(n + l)Γ(β + l)Γ(α) έi Γ(k+l)Γ(a+β+n+k+2) Sk ' and the (C t , a, β) transformation of the function s(x) is defined by Q(y) _ na + β + ΐ)