Decomposition formulas for the double hypergeometric functions G1 and G2

With the help of Burchnall and Chaundy operator method the Decomposition for Hypergeometric G1 (α; β1, β2; x, y),  G2 (α1, α2, β1, β2; x, y) functions have been found. The obtained Decomposition consists of Hypergeometric of Appell's functions. Further, the found decomposition is used for determination of Integral Representation such as Euler type of Hypergeometric G1 (α; β1,  β2; x, y), G2 (α1, α2, β1, β2; x, y) functions.