## The Many Faces of the Polygamma Function

**Authors:** Simon Plouffe

A survey is made based on finite sums of the polygamma function with rational arguments which are D_(k,j)^n=∑_((m,n)=1)▒〖χ_j (n)ψ(k,m/n) 〗 Where, χ_j (n) is the j’th Dirichlet character and ψ(k,m/n) is the polygamma function of order k. We use this representation to rewrite identities using a new notation for linear combinations of mathematical constants. Identities are given for prime numbers using irrational constants. For negative argument n we use the generalization of Espinosa and Moll[6], well implemented into Maple CAS.

**Comments:** A minor correction on page 2

**Download:** **PDF**

### Submission history

[v1] 2016-03-31 22:44:34

[v2] 2018-08-13 13:46:02

**Unique-IP document downloads:** 291 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*