Confluent Hypergeometric Differential Equation

The second-order ordinary differential equation


sometimes also called Kummer's differential equation (Slater 1960, p. 2; Zwillinger 1997, p. 124). It has a regular singular point at 0 and an irregular singularity at infty. The solutions


are called confluent hypergeometric function of the first and second kinds, respectively. Note that the confluent hypergeometric function of the first kind is also denoted M(a,c,x) or Phi(a;c;z).

See also

Confluent Hypergeometric Function of the First Kind, Confluent Hypergeometric Function of the Second Kind, General Confluent Hypergeometric Differential Equation, Hypergeometric Differential Equation, Whittaker Differential Equation

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Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 504, 1972.Arfken, G. "Confluent Hypergeometric Functions." §13.6 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 753-758, 1985.Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 551-555, 1953.Slater, L. J. Confluent Hypergeometric Functions. Cambridge, England: Cambridge University Press, 1960.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 123-124, 1997.

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Confluent Hypergeometric Differential Equation

Cite this as:

Weisstein, Eric W. "Confluent Hypergeometric Differential Equation." From MathWorld--A Wolfram Web Resource.

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