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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1850225577031630848 |
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| author | L. R. Bragg |
| author_facet | L. R. Bragg |
| author_sort | L. R. Bragg |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-58a3e9788c244b4ea35027930c4b08cc |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1989-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-58a3e9788c244b4ea35027930c4b08cc2025-08-20T02:05:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-0112358358710.1155/S0161171289000712Some series whose coefficients involve the value ζ(n) for $n$n oddL. R. Bragg0Department of Mathematical Sciences, Oakland University, Rochester 48309, Michigan, USABy 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.http://dx.doi.org/10.1155/S0161171289000712 |
| spellingShingle | L. R. Bragg Some series whose coefficients involve the value ζ(n) for $n$n odd International Journal of Mathematics and Mathematical Sciences |
| title | Some series whose coefficients involve the value ζ(n) for $n$n odd |
| title_full | Some series whose coefficients involve the value ζ(n) for $n$n odd |
| title_fullStr | Some series whose coefficients involve the value ζ(n) for $n$n odd |
| title_full_unstemmed | Some series whose coefficients involve the value ζ(n) for $n$n odd |
| title_short | Some series whose coefficients involve the value ζ(n) for $n$n odd |
| title_sort | some series whose coefficients involve the value ζ n for n n odd |
| url | http://dx.doi.org/10.1155/S0161171289000712 |
| work_keys_str_mv | AT lrbragg someserieswhosecoefficientsinvolvethevalueznfornnodd |