/(dz)-aby=0.](/images/equations/HypergeometricDifferentialEquation/NumberedEquation1.svg) |
It has regular singular points at 0, 1, and 
.
Every second-order ordinary
differential equation with at most three regular
singular points can be transformed into the hypergeometric differential equation.
Hypergeometric Differential Equation
See also
Confluent Hypergeometric Differential Equation, Confluent Hypergeometric Function of the First Kind, Generalized Hypergeometric Function, Hypergeometric FunctionExplore with Wolfram|Alpha
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 EquationCite this as:
Weisstein, Eric W. "Hypergeometric Differential Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HypergeometricDifferentialEquation.html