A continued fraction expansion for a generalization of Dawson's integral

Author:
D. Dijkstra

Journal:
Math. Comp. **31** (1977), 503-510

MSC:
Primary 40A15

DOI:
https://doi.org/10.1090/S0025-5718-1977-0460956-3

MathSciNet review:
0460956

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Abstract: A continued fraction expansion for a generalization of Dawson's integral is presented. An exact formula for the truncation error in terms of the confluent hypergeometric function is derived. The expansion is shown to have good convergence properties for both small and large values of the argument.

**[1]**M. ABRAMOWITZ & I. A. STEGUN (Editors),*Handbook of Mathematical Functions, With Formulas, Graphs and Mathematical Tables*, Nat. Bur. Standards, Appl. Math. Ser., no. 55, Superintendent of Documents, U. S. Government Printing Office, Washington, D. C., 1966. MR**34**#8607. MR**0167642 (29:4914)****[2]**J. H. McCABE, "A continued fraction expansion, with a truncation error estimate, for Dawson's integral,"*Math. Comp.*, v. 28, 1974, pp. 811-816. MR**51**#7243. MR**0371020 (51:7243)****[3]**P. WYNN, "The numerical efficiency of certain continued fraction expansions. IA, IB,"*Nederl. Akad. Wetensch. Proc. Ser. A*, v. 65 =*Indag. Math.*, v. 24, 1962, pp. 127-137, 138-148. MR**25**#2690a, b. MR**0139254 (25:2690a)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0460956-3

Keywords:
Continued fractions,
confluent hypergeometric functions,
truncation error

Article copyright:
© Copyright 1977
American Mathematical Society