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The polygamma function $\psi\sp{(k)}(x)$ for $x={1\over 4}$ and $x={3\over 4}$. (English) Zbl 0860.33002
Summary: Expressions for the polygamma function $\psi^{(k)}(x)$ for the arguments $x={1\over 4}$ and $x={3\over 4}$ are given in terms of Bernoulli numbers, Euler numbers, the Riemann zeta function for odd integer arguments, and the related series of reciprocal powers of integers $\beta(m)$.

33B15Gamma, beta and polygamma functions
Full Text: DOI
[1] Abramowitz, M.; Stegun, I.A.: Handbook of mathematical functions with formulas, graphs, and mathematical tables. (1972) · Zbl 0543.33001
[2] de Doelder, P.J.: On the clausen integral cl2({$\theta$}) and a related integral. J. comput. Appl. math. 11, 325-330 (1984) · Zbl 0553.33005
[3] Gradshteyn, I.S.; Ryzhik, I.M.: Jeffreya.table of integrals, series and products. Table of integrals, series and products (1994) · Zbl 0918.65002
[4] E.B. Krupnikov, Private communication.