Hypergeometric Function
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 Definition The Gaussian Hypergeometric Differential Equation is: where , , and are constants. The indicial equation of the hypergeometric differential equation is: which has the roots and . Using the Frobenius method, the series solution for can be express as: where 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 General Solution: If , , and are all non-integers, the general solution for the hypergeometric differential equation is: which is valid for . Gamma Function: A hypergeometric function can be expressed in terms of gamma functions. For , Other Formulas:
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