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Numerical calculation of certain definite integrals by Poisson's summation formula


Author: Henry E. Fettis
Journal: Math. Comp. 9 (1955), 85-92
MSC: Primary 65.0X
DOI: https://doi.org/10.1090/S0025-5718-1955-0072546-0
MathSciNet review: 0072546
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References [Enhancements On Off] (What's this?)

  • [1] E. C. Titchmarsh, Theory of Functions, Oxford Univ. Press, London, 1939.
  • [2] Smithsonian Mathematical Formulae and Tables of Elliptic Functions, Smithsonian Institution, Washington, 1922.
  • [3] H. B. Dwight, Tables of Integrals and Other Mathematical Data, Macmillan, New York, 1947. MR 0129577 (23:B2613)
  • [4] A. Erdélyi, W. Magnus, F. Oberhettinger, & F. G. Tricomi, Tables of Integral Transforms, McGraw-Hill, New York, 1954.
  • [5] A. Erdélyi, W. Magnus, F. Oberhettinger, & F. G. Tricomi, Higher Transcendental Functions, vol. 2, McGraw-Hill, New York, 1954.
  • [6] Wilhelm Magnus & Fritz Oberhettinger, Formeln und Sätze für die Speziellen Funktionen der Mathematischen Physik, Springer, Berlin, 1948. MR 0025629 (10:38a)
  • [7] F. Jahnke & F. Emde, Tables of Functions, Dover, New York, 1945.
  • [8] NBSCL, Tables of Bessel Functions $ {Y_0}(z)$ and $ {Y_1}(z)$ for Complex Arguments, Columbia Press, New York, 1950.
  • [9] NBS Applied Mathematics Series No. 23, Tables of the Normal Probability Function, U. S. Govt. Printing Office, Washington, 1953.
  • [10] L. Schwarz, Untersuchung einiger mit den Zylinderfunktionen nullter Ordnung verwandter Funktionen. Luftfahrtforschung, v. 20, 1944, p. 341-372. MR 0010017 (5:238d)
  • [11] G. N. Watson, A Treatise on the Theory of Bessel Functions, Macmillan, New York, 1948. MR 0010746 (6:64a)
  • [12] For those values of $ z$ and $ n$ which are of interest here, the difference between $ {\log _{10}}{J_n}(z)$ and $ {\log _{10}}{I_n}(z)$ is approximately equal to $ {z^2}{\log _{10}}e/2(n + 1)$.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1955-0072546-0
Article copyright: © Copyright 1955 American Mathematical Society

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