Higher-order recurrences for Bernoulli numbers |
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| Authors: | Takashi Agoh |
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| Affiliation: | a Department of Mathematics, Tokyo University of Science, Noda, Chiba, 278-8510, Japan
b Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada |
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| Abstract: | Euler's well-known nonlinear relation for Bernoulli numbers, which can be written in symbolic notation as n(B0+B0)=−nBn−1−(n−1)Bn, is extended to n(Bk1+?+Bkm) for m?2 and arbitrary fixed integers k1,…,km?0. In the general case we prove an existence theorem for Euler-type formulas, and for m=3 we obtain explicit expressions. This extends the authors' previous work for m=2. |
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