## 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:** 14 Pages. news identities for primes, binomial sums and euler, bernoulli numbers

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### Submission history

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

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