double gamma function

The digamma function is a special function which is given by the logarithmic derivative of the gamma function (or, depending on the definition, the logarithmic derivative of the factorial). Because of this ambiguity, two different notations are sometimes (but not always) used, with Ψ(z) congruent d/(d z) ln Γ(z) = (Γ'(z))/(Γ(z)) defined as the logarithmic derivative of the gamma function Γ(z), and F(z) congruent d/(d z) ln z!

Barnes G-function | gamma function | Gauss's digamma theorem | G-function | harmonic number | Hurwitz zeta function | logarithmic derivative | Mellin's formula | polygamma function | Ramanujan ϕ-function | trigamma function