Hardy space of Clausen's and Goursat's hypergeometric functions - Jocelyn Johnson; S. Sunil Varma (Surveys in Mathematics and its Applications)
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.