differential-difference equations for hypergeometric function
The hypergeometric function satisfies several equations which
relate derivatives with respect to the argument to
shifting the parameters by unity (Here, the
prime denotes derivative with respect to .):
These equations may readily be verified by differentiating the series
which defines the hypergeometric equation. By eliminating the derivatives
between these equations, one obtains the contiguity relations for the
hypergeometric function. By differentiating them once more and taking
suitable linear combinations
, one may obtain the differential equation
of the hypergeometric function.
Title | differential-difference equations for hypergeometric function |
---|---|
Canonical name | DifferentialdifferenceEquationsForHypergeometricFunction |
Date of creation | 2013-03-22 17:36:18 |
Last modified on | 2013-03-22 17:36:18 |
Owner | rspuzio (6075) |
Last modified by | rspuzio (6075) |
Numerical id | 6 |
Author | rspuzio (6075) |
Entry type | Theorem |
Classification | msc 33C05 |