The W-transform of a function f(x) is defined by the integral (W f)(x) = (W_(p q)^(m n) left bracketing bar ν, (α)_p (β_q) right bracketing bar f(t))(x) = 1/(2π i) integral_σ Γ(ν - i x - s, ν + i x - s) Γ[(β_m) + s, | 1 - (α_n) - s (α_p^(n + 1)) + s, | 1 - (β_q^(m + 1)) - s] f^*(1 - s) d s, where