## Confluent Hypergeometric Differential Equation

 (1)

where and with boundary conditions
 (2)

 (3)

The equation has a Regular Singular Point at 0 and an irregular singularity at . The solutions are called Confluent Hypergeometric Function of the First or Second Kinds. Solutions of the first kind are denoted or .

References

Abramowitz, M. and Stegun, C. 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.