- Acta Math.
- Volume 83 (1950), 131-164.
Hypergeometric functions of two variables
The systematic investigation of contour integrals satisfying the system of partial differential equations associated with Appell's hypergeometric function F1 leads to new solutions of that system. Fundamental sets of solutions are given for the vicinity of all singular points of the system of partial differential equations. The transformation theory of the solutions reveals connections between the system under consideration and other hypergeometric systems of partial differential equations. Presently it is discovered that any hypergeometric system of partial differential equations of the second order (with two independent variables) which has only three linearly independent solutions can be transformed into the system of F1 or into a particular or limiting case of this system. There are also other hypergeometric systems (with four linearly independent solutions) the integration of which can be reduced to the integration of the system of F1.
Acta Math., Volume 83 (1950), 131-164.
First available in Project Euclid: 31 January 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
1964 © Almqvist & Wiksells Boktryckeri
Erdélyi, A. Hypergeometric functions of two variables. Acta Math. 83 (1950), 131--164. doi:10.1007/BF02392635. https://projecteuclid.org/euclid.acta/1485888583