On a new class of double integrals involving hypergeometric function

The aim of this research paper is to provide a large number of double integrals in the form of four master formulas. A large number of very interesting integrals follow special cases of our main findings. These results are obtained with the help of contiguous extensions of classical summation theorems such as of Watson, Dixon and Whipple on the sum of a (3)F(2). The double integrals established in this paper are simple, interesting, easily established and may be useful.