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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A method for the computation of the Fresnel integrals and related functions
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by Oscar L. Fleckner PDF
Math. Comp. 22 (1968), 635-640 Request permission

Abstract:

A new method for computing the values of the Fresnel integrals and related functions is developed. Error estimates for the resulting power series are derived, and an application of the technique is discussed.
References
  • Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D.C., 1964. For sale by the Superintendent of Documents. MR 0167642
  • R. Courant, Differential and Integral Calculus, Vols. I, II, Interscience, New York, 1960.
  • Walter Gautschi, Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24–82. MR 213062, DOI 10.1137/1009002
  • C. D. Hodgman, C. R. C. Standard Mathematical Tables, Chemical Rubber Publishing Co., Cleveland, Ohio, 1959.
  • Eugene Jahnke, Fritz Emde, and Friedrich Lösch, Tables of higher functions, McGraw-Hill Book Co., Inc., New York-Toronto-London; B. G. Teubner Verlagsgesellschaft, Stuttgart, 1960. 6th ed; Revised by Friedrich Lösch. MR 0114317
  • T. Pearcey, Table of the Fresnel Integrals, Commonwealth Scientific and Industrial Research Organization, Melbourne, Australia, 1956. SCATRAN Reference Manual, Numerical Computation Laboratory, The Ohio State University, 1964.
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Additional Information
  • © Copyright 1968 American Mathematical Society
  • Journal: Math. Comp. 22 (1968), 635-640
  • MSC: Primary 65.25
  • DOI: https://doi.org/10.1090/S0025-5718-1968-0226824-1
  • MathSciNet review: 0226824