## The generalization of Faulhaber’s formula to sums of non-integral powers.(English)Zbl 1176.11004

Authors’ summary: “A formula for the sum of any positive-integral power of the first $$N$$ positive integers was published by Johann Faulhaber (1580–1635). In this paper, we generalize Faulhaber’s formula to non-integral complex powers with real part greater than $$-1$$.”
See also the following article of Donald Knuth, Johann Faulhaber and sums of powers. Math. Comput. 61, No. 203, 277–294 (1993; Zbl 0797.11026).

### MSC:

 11B57 Farey sequences; the sequences $$1^k, 2^k, \dots$$ 11M06 $$\zeta (s)$$ and $$L(s, \chi)$$

Zbl 0797.11026
Full Text:

### References:

 [1] Conway, John; Guy, Richard, The book of numbers, (1996), Springer-Verlag New York, p. 106 · Zbl 0866.00001 [2] Ivić, Aleksandar, The Riemann zeta-function: the theory of the Riemann zeta-function with applications, (1985), John Wiley & Sons New York · Zbl 0556.10026 [3] Parks, Harold R., Sums of non-integral powers, J. math. anal. appl., 297, 343-349, (2004) · Zbl 1160.11310
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