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单词 Confluent Hypergeometric Differential Equation
释义

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 calledConfluent Hypergeometric Function of the First orSecond Kinds. Solutions of the first kind are denoted or .

See also Hypergeometric Differential Equation, Whittaker Differential Equation


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.


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