Some series whose coefficients involve the value ζ(n) for $n$n odd
By using two basic formulas for the digamma function, we derive a variety of series that involve as coefficients the values (2n+1), n=1,2,⋯, of the Riemann-zeta function. A number of these have a combinatorial flavor which we also express in a trignometric form for special choices of the underlying...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289000712 |
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| Summary: | By using two basic formulas for the digamma function, we derive a variety
of series that involve as coefficients the values (2n+1), n=1,2,⋯, of the
Riemann-zeta function. A number of these have a combinatorial flavor which we also
express in a trignometric form for special choices of the underlying variable. We
briefly touch upon their use in the representation of solutions of the wave equation. |
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| ISSN: | 0161-1712 1687-0425 |