A New Method for Investigating Euler Sums |
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| Authors: | Basu Ankur Apostol Tom M. |
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| Affiliation: | (1) 82A Ramprasad Chattergee Road, Narua, P.O. Chandannagar, Dist. Hoogly, PIN-712136 West Bengal, India;(2) Department of Mathematics, California Institute of Technology, Pasadena, California, 91125 |
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| Abstract: | Euler discovered a recursion formula for the Riemann zeta function evaluated at the even integers. He also evaluated special Dirichlet series whose coefficients are the partial sums of the harmonic series. This paper introduces a new method for deducing Euler's formulas as well as a host of new relations, not only for the zeta function but for several allied functions. |
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| Keywords: | Riemann zeta function Euler sums recursion formulas |
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