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: