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 . 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 or .

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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References 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. Referenced on Wolfram|Alpha Confluent
Hypergeometric Differential Equation
Cite this as:
Weisstein, Eric W. "Confluent Hypergeometric Differential Equation." From MathWorld --A Wolfram Web
Resource. https://mathworld.wolfram.com/ConfluentHypergeometricDifferentialEquation.html

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