A special function ψ_1(z) corresponding to a polygamma function ψ_n(z) with n = 1, given by ψ_1(z) congruent d^2/(d z^2) ln Γ(z). An alternative function F'(z) congruent d^2/(d z^2) ln z! is sometimes called the trigamma function, where F'(z) = ψ_1(z + 1). Sums and differences of ψ_1(r/s) for small integers r and s can be expressed in terms of π, Catalan's constant K, and Clausen functions.
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