Trigamma Function

Min Max Re Im

A special function corresponding to a polygamma function with , given by

(1)

An alternative function

(2)

is sometimes called the trigamma function, where

(3)

Sums and differences of for small integers and can be expressed in terms of , Catalan's constant , and Clausen functions. For example,

			(4)
			(5)
			(6)
			(7)
			(8)
			(9)
			(10)
			(11)
			(12)
			(13)

In general,

(14)

(Lewin 1991).