Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients
This paper studies reciprocals of formal power series whose coefficients are monotone and bounded by a geometrically decaying sequence. Explicit and applicable, optimal decay rates are provided for the coefficients of the reciprocal series in terms of the parameters of the geometric bound. The resul...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/40270 |
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| _version_ | 1832562506288070656 |
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| author | Kenneth S. Berenhaut Edward E. Allen Sam J. Fraser |
| author_facet | Kenneth S. Berenhaut Edward E. Allen Sam J. Fraser |
| author_sort | Kenneth S. Berenhaut |
| collection | DOAJ |
| description | This paper studies reciprocals of formal power series whose coefficients
are monotone and bounded by a geometrically decaying sequence. Explicit
and applicable, optimal decay rates are provided for the coefficients of the reciprocal
series in terms of the parameters of the geometric bound. The results imply a
best possible lower bound on the zeros of the series being considered. |
| format | Article |
| id | doaj-art-e656eb69f3b04610850a6366ee2c9823 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e656eb69f3b04610850a6366ee2c98232025-02-03T01:22:31ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/4027040270Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficientsKenneth S. Berenhaut0Edward E. Allen1Sam J. Fraser2Department of Mathematics, Wake Forest University, Winston-Salem 27109, NC, USADepartment of Mathematics, Wake Forest University, Winston-Salem 27109, NC, USADepartment of Mathematics, Wake Forest University, Winston-Salem 27109, NC, USAThis paper studies reciprocals of formal power series whose coefficients are monotone and bounded by a geometrically decaying sequence. Explicit and applicable, optimal decay rates are provided for the coefficients of the reciprocal series in terms of the parameters of the geometric bound. The results imply a best possible lower bound on the zeros of the series being considered.http://dx.doi.org/10.1155/DDNS/2006/40270 |
| spellingShingle | Kenneth S. Berenhaut Edward E. Allen Sam J. Fraser Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients Discrete Dynamics in Nature and Society |
| title | Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients |
| title_full | Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients |
| title_fullStr | Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients |
| title_full_unstemmed | Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients |
| title_short | Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients |
| title_sort | bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients |
| url | http://dx.doi.org/10.1155/DDNS/2006/40270 |
| work_keys_str_mv | AT kennethsberenhaut boundsoncoefficientsofreciprocalsofformalpowerserieswithrapidlydecreasingcoefficients AT edwardeallen boundsoncoefficientsofreciprocalsofformalpowerserieswithrapidlydecreasingcoefficients AT samjfraser boundsoncoefficientsofreciprocalsofformalpowerserieswithrapidlydecreasingcoefficients |