Trigamma function
In mathematics, the trigamma function, denoted ψ1(z) or ψ(1)(z), is the second of the polygamma functions, and is defined by ψ 1 ( z ) = d 2 d z 2 ln Γ ( z ) {\displaystyle \psi _{1}(z)={\frac {d^{2}}{dz^{2}}}\ln \Gamma (z)} . It follows from this definition that ψ 1 ( z ) = d d z ψ ( z ) {\displaystyle \psi _{1}(z)={\frac {d}{dz}}\psi (z)} where ψ(z) is the digamma function.