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XXII.—Integration of a Certain System of Linear Partial Differential Equations of Hypergeometric Type

Published online by Cambridge University Press:  15 September 2014

A. Erdélyi
A. Erdélyi
Affiliation:
Mathematical Institute, University of Edinburgh
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1. The integration of systems of linear partial differential equations of hypergeometric type has been the subject of a great number of recent investigations (e.g. Appell, 1925; Appell-Kampé de Fériet, 1926). Especially Professor Horn (see references) and his pupils, for instance Borngässer (1933), have done much valuable work in this field.

The first method that suggests itself for integrating systems of this type is to try power-series expansions of the solutions in the neighbourhood of the singular points of the system. This method, however, does not yield in general a complete set of solutions. Those singular points of the system in which more than n singular manifolds intersect, n being the number of independent variables, give rise to considerable difficulties.

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Proceedings
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Proceedings of the Royal Society of Edinburgh , Volume 59 , 1940 , pp. 224 - 241
Copyright
Copyright © Royal Society of Edinburgh 1940

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References

References to Literature

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