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 . 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 .

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.