On the overconvergence of certain series
In this work, we consider certain class of exponential series with polynomial coefficients and study the properties of convergence of such series. Then we consider a subclass of this class and prove certain theorems on the overconvergence of such a series, which allow us to determine the conditions...
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| Format: | Article |
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Hindawi Limited
1979-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171279000053 |
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doaj-3c1948348c244d34bc2a6c6267332ff22020-11-24T22:43:45ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-0121456010.1155/S0161171279000053On the overconvergence of certain seriesM. Blambert0R. Parvatham1Institut Fourier, Mathématiques Pures, Boite postale 116, St Martin d'Heres 38402, FranceInstitut Fourier, Mathématiques Pures, Boite postale 116, St Martin d'Heres 38402, FranceIn this work, we consider certain class of exponential series with polynomial coefficients and study the properties of convergence of such series. Then we consider a subclass of this class and prove certain theorems on the overconvergence of such a series, which allow us to determine the conditions under which the boundary of the region of convergence of this series is a natural boundary for the function f defined by this series.http://dx.doi.org/10.1155/S0161171279000053LC-dirichletian elementL-dirichletian elementconvergenceoverconvergence. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. Blambert R. Parvatham |
| spellingShingle |
M. Blambert R. Parvatham On the overconvergence of certain series International Journal of Mathematics and Mathematical Sciences LC-dirichletian element L-dirichletian element convergence overconvergence. |
| author_facet |
M. Blambert R. Parvatham |
| author_sort |
M. Blambert |
| title |
On the overconvergence of certain series |
| title_short |
On the overconvergence of certain series |
| title_full |
On the overconvergence of certain series |
| title_fullStr |
On the overconvergence of certain series |
| title_full_unstemmed |
On the overconvergence of certain series |
| title_sort |
on the overconvergence of certain series |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1979-01-01 |
| description |
In this work, we consider certain class of exponential series with polynomial coefficients and study the properties of convergence of such series. Then we consider a subclass of this class and prove certain theorems on the overconvergence of such a series, which allow us to determine the conditions under which the boundary of the region of convergence of this series is a natural boundary for the function f defined by this series. |
| topic |
LC-dirichletian element L-dirichletian element convergence overconvergence. |
| url |
http://dx.doi.org/10.1155/S0161171279000053 |
| work_keys_str_mv |
AT mblambert ontheoverconvergenceofcertainseries AT rparvatham ontheoverconvergenceofcertainseries |
| _version_ |
1725694832499752960 |