Trigamma Function

The trigamma function is the second of the polygamma functions, defined as the derivative of the digamma function, which is itself the logarithmic derivative of the Gamma function. It can be written as an infinite sum of the reciprocals of (n+x) squared over all non-negative integers n, and its value at 1 equals pi squared over 6, matching the Basel problem's sum of reciprocal squares. The trigamma function appears in the asymptotic expansion of the Gamma function, in statistics through the Fisher information of certain distributions, and in the evaluation of specific infinite series. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/