Values of the polygamma functions at rational arguments. (English) Zbl 1127.33002
The values of psi (or digamma) function and its derivatives, polygamma function, at rational arguments in terms of elementary functions are known due to a number of authors. In this paper the authors re-find (and re-prove) above mentioned values in terms of other functions such as the Hurwitz zeta function, Bernoulli polynomials and Clausen functions.
Reviewer: Mehdi Hassani (Zanjan)
MSC:
33B15 | Gamma, beta and polygamma functions |
11M35 | Hurwitz and Lerch zeta functions |
11B68 | Bernoulli and Euler numbers and polynomials |