Hardy space of Clausen's and Goursat's hypergeometric functions
Let ℛ denote the class of analytic functions defined in the open unit disc Δ=\z∈ ℂ: |z|<1\ whose derivative has positive real part and H∞ be the space of all bounded analytic functions defined in the open unit disc. In this research article we determine the conditions on the parameters of Clausen...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University Constantin Brancusi of Targu-Jiu
2025-04-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | https://www.utgjiu.ro/math/sma/v20/p20_10.pdf |
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| Summary: | Let ℛ denote the class of analytic functions defined in the open unit disc Δ=\z∈ ℂ: |z|<1\ whose derivative has positive real part and H∞ be the space of all bounded analytic functions defined in the open unit disc. In this research article we determine the conditions on the parameters of Clausen's hypergeometric function, 3F2(a,b,c;d,e;z) and Goursat's hypergeometric function, 2F2(a,b;c,d;z) so that the convolution of z3F2(a,b,c;d,e;z) and z2F2(a,b;c,d;z) with a function in ℛ belong to H∞ ∩ ℛ. |
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| ISSN: | 1843-7265 1842-6298 |