Appell functions of matrix arguments (Q1355407)

The authors define Appell's functions \(F_1\), \(F_2\), \(F_3\) of two matrix arguments in terms of double integrals of matrix arguments and derive integral representations for these functions. The paper is concluded with the remark that the Appell functions considered in the paper are invariant under the simultaneous transformations \[ X\to H'XH,\quad Y\to H'YH, \] where \(X\) and \(Y\) are matrix arguments as real symmetric positive definite matrices and \(H\) is an orthogonal matrix.