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Mathematics of Computation

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Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials


Author: Richard Barakat
Journal: Math. Comp. 15 (1961), 7-11
MSC: Primary 65.25
MathSciNet review: 0128058
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  • [1] Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger, and Francesco G. Tricomi, Higher transcendental functions. Vols. I, II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953. Based, in part, on notes left by Harry Bateman. MR 0058756
  • [2] G. N. Watson, Treatise on the Theory of Bessel Functions, Second Edition, Cambridge University Press, 1948, p. 544.
  • [3] Erwin Kreyszig, On the zeros of the Fresnel integrals, Canad. J. Math. 9 (1957), 118–131. MR 0090679
  • [4] C. Lanczos, Tables of Chebyshev Polynomials $ {S_n}(x)$ and $ {C_n}(x)$, Nat. Bur. Standards, U. S. Government Printing Office, Washington D. C., 1952.
  • [5] B. van der Pol & T. J. Weijers, ``Tchebycheff Polynomials and Their Relation to Circular Functions, Bessel Functions and Lissajous Figures,'' Physica, 1933.
  • [6] N. W. McLachlan, Bessel Functions for Engineers, Second Edition, Oxford University Press, 1955, p. 86.
  • [7] T. Pearcey, Table of the Fresnel integral to six decimal places, Cambridge University Press, New York, 1956. MR 0084206

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DOI: https://doi.org/10.1090/S0025-5718-1961-0128058-1
Article copyright: © Copyright 1961 American Mathematical Society