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The generalization of Faulhaber's formula to sums of non-integral powers |
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| Authors: | Kevin J McGown |
| Institution: | a Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112, USA b Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605, USA |
| Abstract: | A formula for the sum of any positive-integral power of the first N positive integers was published by Johann Faulhaber in the 1600s. In this paper, we generalize Faulhaber's formula to non-integral complex powers with real part greater than −1. |
| Keywords: | Sums of non-integral powers Faulhaber's formula Bernoulli numbers Euler-Maclaurin summation Riemann zeta function |
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