Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 20 (2025), 203 -- 216

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This work is licensed under a Creative Commons Attribution 4.0 International License.

HARDY SPACE OF CLAUSEN'S AND GOURSAT'S HYPERGEOMETRIC FUNCTIONS

Jocelyn Johnson and S. Sunil Varma

Abstract. 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.

2020 Mathematics Subject Classification: Primary: 30H10; Secondary: 30H05, 33C20, 30C45.
Keywords: Analytic functions, Hardy spaces, Clausen's hypergeometric function, Goursat's hypergeometric function.

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Jocelyn Johnson
Department of Mathematics,
Madras Christian College (University of Madras),
600059, East Tambaram, Tamil Nadu, India.
e-mail: jocelynjohnson1010@gmail.com


S. Sunil Varma
Department of Mathematics,
Madras Christian College (University of Madras),
600059, East Tambaram, Tamil Nadu, India.
e-mail: sunilvarma@mcc.edu.in



https://www.utgjiu.ro/math/sma