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
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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 ${z^2}{\log _{10}}e/2(n + 1)$.
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