Generalized Hypergeometric Differential Equation
The generalized hypergeometric function
![👁 F(x)=_pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;x]](https://mathworld.wolfram.com/images/equations/GeneralizedHypergeometricDifferentialEquation/NumberedEquation1.svg){kind=link}
satisfies the equation
where 👁 theta=x(partial/partialx)
is the differential
operator.
See also
Generalized Hypergeometric FunctionExplore with Wolfram|Alpha
References
Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, p. 26, 1998.Miller, W. Jr. Symmetry and Separation of Variables. Reading, MA: Addison-Wesley, p. 271, 1977.Rainville, E. D. Special Functions. New York: Chelsea, 1971.Slater, L. J. Confluent Hypergeometric Functions. Cambridge, England: Cambridge University Press, p. 1, 1960.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 128, 1997.Referenced on Wolfram|Alpha
Generalized Hypergeometric Differential EquationCite this as:
Weisstein, Eric W. "Generalized Hypergeometric Differential Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeneralizedHypergeometricDifferentialEquation.html