ToHypergeometric

Description

ToHypergeometric[(t^b) (((1 - t))^c) (((1 + t z))^a), t] returns Γ(b + 1) Γ(c + 1)/Γ(b + c + 2) (Subscript[, 2]) (Subscript[F, 1])(-a, b + 1; 
                b + c + 2; -z). Remember that Re b >0 and Re (c-b) > 0 should hold (need not be set in Mathematica).

See also:  HypergeometricAC, HypergeometricIR, HypergeometricSE.

Examples

ToHypergeometric[(t^b) (((1 - t))^c) (((1 + t z))^a), t]

ToHypergeometric[
      w (t^(b - 1)) (((1 - t))^(c - b - 1)) (((1 - t z))^(-a)), 
      t]

ToHypergeometric[(t^b) (((1 - t))^c) (((u + t z))^a), t]

ToHypergeometric[
      w (t^(b - 1)) (((1 - t))^(c - b - 1)) (((u - t z))^(-a)), 
      t]