| Definition |
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The Gaussian Hypergeometric Differential Equation is:  where  which has the roots  where  |
, 
, and 
are constants. The indicial equation of the hypergeometric differential equation is:
and 
. Using the Frobenius method, the series solution for 
and the series converges for 
. This series is called Hypergeometric Series. The sum of the hypergeometric series denoted by 
is called Hypergeometric Function, which is:| Important Properties |
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General Solution: If  which is valid for Gamma Function: A hypergeometric function can be expressed in terms of gamma functions.  For  Other Formulas:   |
, and 
are all non-integers, the general solution for the hypergeometric differential equation is:
,| Special Results | ||||||||||
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