Closed form general solution of the hypergeometric matrix differential equation

✍ Scribed by L. Jódar; J.C. Cortés

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 778 KB
• Volume: 32
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(00)00187-4

✦ Synopsis

In this paper, the hypergeometric matrix differential equation z( 1 -t)W" -zAW' + W'(C -z(B + I)) -AWB = 0 is studied. First it is proved that if matrix C is invertible and no negative integer is one of its eigenvalues, then the hypergeometric matrix function F(A, B; C; z) is an analytic solution in the unit disc. If, apart from the above hypothesis on C, matrices A and B commute with C, then a closed form general solution is expressed in terms of F(A, B; C; z) and F(A+I-C,B+I-C;~I-C;Z)~-~ in n(6) = {z E DO, 0 < 1.~1 < a}, where DO is the complex plane cut along the negative real axis, and 6 > 0 is a positive number determined in terms of the data.