LINEARLY INDEPENDENT SOLUTIONS FOR THE HYPERGEOMETRIC EXTON FUNCTIONS X1 AND X2

In investigation of boundary-value problems for certainpartial dierential equations arising in applied mathematics, weoften need to study the solution of system of partial dierentialequations satised by hypergeometric functions and nd explicitlinearly independent solutions for the system. Here we choose theExton functions X1 and X2 among his twenty functions to showhow to nd the linearly independent solutions of partial di erentialequations satised by these functions X1 and X2.