In order to obtain the linear relations among the 24-solutions for the p-differential equation of Riemann, Barnes [12] discovered an elegant method which uses the following identity for the classical Γ function.

For complex numbers α, β, γ, δ the equality

formula here

holds and the path of integration from −i∞ to +i∞ is curved so that the poles of Γ(γ−s) Γ(δ−s) lie on the right and the poles of Γ(α+s) Γ(β+s) lie on the left.