Hardy space of Clausen's and Goursat's hypergeometric functions

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.

Keywords

• analytic functions
• hardy spaces
• clausen's hypergeometric function
• goursat's hypergeometric function