global characterization of hypergeometric function

Riemann noted that the hypergeometric functionDlmfDlmfDlmfMathworldPlanetmath can be characterized by its global properties, without reference to power seriesMathworldPlanetmath, differential equationsMathworldPlanetmath, or any other sort of explicit expression. His characterizationMathworldPlanetmath is conveniently restated in terms of sheaves:

Suppose that we have a sheaf of holomorphic functionsMathworldPlanetmath over {0,1} which satisfy the following properties:

Then the sheaf consists of solutions to a hypergeometric equation, hence the function elementsMathworldPlanetmath are hypergeometric functions.

Title global characterization of hypergeometric function
Canonical name GlobalCharacterizationOfHypergeometricFunction
Date of creation 2014-12-31 15:15:16
Last modified on 2014-12-31 15:15:16
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 6
Author rspuzio (6075)
Entry type Definition
Classification msc 33C05