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Hypergeometric Differential Equation

A hypergeometric differential equation is given by

z(1-z)(d^2y)/(dz^2)+[c-(a+b+1)z](dy)/(dz)-aby=0.

It has regular singular points at 0, 1, and infty. Every second-order ordinary differential equation with at most three regular singular points can be transformed into the hypergeometric differential equation.

See also

Confluent Hypergeometric Differential Equation, Confluent Hypergeometric Function of the First Kind, Generalized Hypergeometric Function, Hypergeometric Function

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References

Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: University Press, pp. 1-2, 1935.Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 542-543, 1953.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 123, 1997.

Referenced on Wolfram|Alpha

Hypergeometric Differential Equation

Cite this as:

Weisstein, Eric W. "Hypergeometric Differential Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HypergeometricDifferentialEquation.html

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