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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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Numerical calculation of certain definite integrals by Poisson’s summation formula
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by Henry E. Fettis PDF
Math. Comp. 9 (1955), 85-92 Request permission
References
    E. C. Titchmarsh, Theory of Functions, Oxford Univ. Press, London, 1939. Smithsonian Mathematical Formulae and Tables of Elliptic Functions, Smithsonian Institution, Washington, 1922.
  • Herbert Bristol Dwight, Tables of integrals and other mathematical data, The Macmillan Company, New York, 1961. 4th ed. MR 0129577
  • A. Erdélyi, W. Magnus, F. Oberhettinger, & F. G. Tricomi, Tables of Integral Transforms, McGraw-Hill, New York, 1954. A. Erdélyi, W. Magnus, F. Oberhettinger, & F. G. Tricomi, Higher Transcendental Functions, vol. 2, McGraw-Hill, New York, 1954.
  • Wilhelm Magnus and Fritz Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1948 (German). 2d ed. MR 0025629, DOI 10.1007/978-3-662-01222-2
  • F. Jahnke & F. Emde, Tables of Functions, Dover, New York, 1945. NBSCL, Tables of Bessel Functions ${Y_0}(z)$ and ${Y_1}(z)$ for Complex Arguments, Columbia Press, New York, 1950. NBS Applied Mathematics Series No. 23, Tables of the Normal Probability Function, U. S. Govt. Printing Office, Washington, 1953.
  • L. Schwarz, Untersuchung einiger mit den Zylinderfunktionen nullter Ordnung verwandter Funktionen, Luftfahrtforschung 20 (1944), 341–372 (German). MR 10017
  • G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
  • 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
  • © Copyright 1955 American Mathematical Society
  • 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