SOME SPECIAL VALUES OF POLYGAMMA FUNCTIONS
Special values of of Polygamma Function We have already seen from previous posts that many infinite series and integrals can be evaluated with techniques that relies on Gamma and Polygamma functions. In view of this fact I decided to proof a few special values for some of these functions to serve primarily as a reference when we encounter them in future computations. It will be a pretty long post but lots of techniques involved, therefore a fun one. Needless to mention their own beauty with expressions involving lots of well known mathematical constants, justifying their derivation just for their own sake. In previous posts we have proved the following relations for the Gamma Function: The recurrence equation of the Gamma Function (1) The reflection formula (2) The duplication formula (3) The triplication formula (4) Additionally, we have already proved the following infinite series representation for the Digamma functio...