The maximum term of a power series
Let ∑n=0∞anzλn be a power series, representing an analytic function f(z) in the disc |z|<R. A characterization for the type of such functions was obtained by the authors [J. Math. Anal. Appl. 81(1981), 1-7] in terms of the maximum term and rank. It is proved in this paper by means of an example,...
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117128600042X |
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| author | G. S. Srivastava O. P. Juneja |
| author_facet | G. S. Srivastava O. P. Juneja |
| author_sort | G. S. Srivastava |
| collection | DOAJ |
| description | Let ∑n=0∞anzλn be a power series, representing an analytic function f(z) in the disc |z|<R. A characterization for the type of such functions was obtained by the authors [J. Math. Anal. Appl. 81(1981), 1-7] in terms of the maximum term and rank. It is proved in this paper by means of an example, that a similar relation does not hold in general for lower type and sufficient conditions have been obtained for the validity of the corresponding result for lower type. Alternative coefficient characterization for type and lower type have been given and a necessary and sufficient condition for the analytic function f(z) to be of perfectly regular growth has been obtained. |
| format | Article |
| id | doaj-art-7eb65a65453744b4aae3c3e757eae954 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7eb65a65453744b4aae3c3e757eae9542025-02-03T07:24:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019234134610.1155/S016117128600042XThe maximum term of a power seriesG. S. Srivastava0O. P. Juneja1Department of Mathematics, University of Roorkee, Roorkee, IndiaDepartment of Mathematics, Indian Institute of Technology, Kanpur, IndiaLet ∑n=0∞anzλn be a power series, representing an analytic function f(z) in the disc |z|<R. A characterization for the type of such functions was obtained by the authors [J. Math. Anal. Appl. 81(1981), 1-7] in terms of the maximum term and rank. It is proved in this paper by means of an example, that a similar relation does not hold in general for lower type and sufficient conditions have been obtained for the validity of the corresponding result for lower type. Alternative coefficient characterization for type and lower type have been given and a necessary and sufficient condition for the analytic function f(z) to be of perfectly regular growth has been obtained.http://dx.doi.org/10.1155/S016117128600042X |
| spellingShingle | G. S. Srivastava O. P. Juneja The maximum term of a power series International Journal of Mathematics and Mathematical Sciences |
| title | The maximum term of a power series |
| title_full | The maximum term of a power series |
| title_fullStr | The maximum term of a power series |
| title_full_unstemmed | The maximum term of a power series |
| title_short | The maximum term of a power series |
| title_sort | maximum term of a power series |
| url | http://dx.doi.org/10.1155/S016117128600042X |
| work_keys_str_mv | AT gssrivastava themaximumtermofapowerseries AT opjuneja themaximumtermofapowerseries AT gssrivastava maximumtermofapowerseries AT opjuneja maximumtermofapowerseries |