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Mathematics of Computation

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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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  • [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] Herbert Bristol Dwight, Tables of integrals and other mathematical data, 4th ed, The Macmillan Company, New York, 1961. MR 0129577
  • [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 and Fritz Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1948 (German). 2d ed. MR 0025629
  • [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 20 (1944), 341–372 (German). MR 0010017
  • [11] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
  • [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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DOI: https://doi.org/10.1090/S0025-5718-1955-0072546-0
Article copyright: © Copyright 1955 American Mathematical Society