Hypergeometric Function - The Hypergeometric Differential Equation

The Hypergeometric Differential Equation

The hypergeometric function is a solution of Euler's hypergeometric differential equation

z(1-z)\frac {d^2w}{dz^2} + \left \frac {dw}{dz} - abw = 0.

which has three regular singular points: 0,1 and ∞. The generalization of this equation to three arbitrary regular singular points is given by Riemann's differential equation. Any second order differential equation with three regular singular points can be converted to the hypergeometric differential equation by a change of variables.

Read more about this topic:  Hypergeometric Function

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