Calculation of the modified Bessel functions of the second kind with complex argument
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References
- Irene A. Stegun and Milton Abramowitz, Generation of Bessel functions on high speed computers, Math. Tables Aids Comput. 11 (1957), 255–257. MR 93939, DOI 10.1090/S0025-5718-1957-0093939-3
- M. Goldstein and R. M. Thaler, Recurrence techniques for the calculation of Bessel functions, Math. Tables Aids Comput. 13 (1959), 102–108. MR 105794, DOI 10.1090/S0025-5718-1959-0105794-5
- C. W. Clenshaw, Chebyshev series for mathematical functions, National Physical Laboratory Mathematical Tables, Vol. 5, Her Majesty’s Stationery Office, London, 1962. Department of Scientific and Industrial Research. MR 0142793
- E. E. Allen, Analytical approximations, Math. Tables Aids Comput. 8 (1954), 240–241. MR 64483, DOI 10.1090/S0025-5718-1954-0064483-1
- A. J. M. Hitchcock, Polynomial approximations to Bessel functions of order zero and one and to related functions, Math. Tables Aids Comput. 11 (1957), 86–88. MR 85598, DOI 10.1090/S0025-5718-1957-0085598-0
- Jet Wimp, Polynomial expansions of Bessel functions and some associated functions, Math. Comp. 16 (1962), 446–458. MR 148956, DOI 10.1090/S0025-5718-1962-0148956-3
- F. D. Burgoyne, Polynomial approximations to $I_{0}\,(x),$ $I_{1} (x)$ and related functions, Math. Comp. 16 (1962), 497–498. MR 147682, DOI 10.1090/S0025-5718-1962-0147682-4
- Henry E. Fettis, Numerical calculation of certain definite integrals by Poisson’s summation formula, Math. Tables Aids Comput. 9 (1955), 85–92. MR 72546, DOI 10.1090/S0025-5718-1955-0072546-0
- Yudell L. Luke, Simple formulas for the evaluation of some higher transcendental functions, J. Math. and Phys. 34 (1956), 298–307. MR 78047, DOI 10.1002/sapm1955341298
- D. B. Hunter, The calculation of certain Bessel functions, Math. Comp. 18 (1964), 123–128. MR 158104, DOI 10.1090/S0025-5718-1964-0158104-3
- Wilhelm Magnus and Fritz Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1943 (German). MR 0022272 I. M. Ryžik & I. S. Gradštein, Tables of integrals, sums, series and products, 3rd ed., GITTL, Moscow, 1951; 4th ed., Fizmatigiz, Moscow, 1963; English and German transl, of 3rd ed., Summen-, Produkt- und Integral-tafeln, VEB Deutscher Verlag der Wissenschaften, Berlin, 1957; 2nd rev. ed. of transl., VEB Deutscher Verlag der Wissenschaften, Berlin and Plenum Press, New York, 1963, Formulas 7.323 and 7.335. MR 14, 643; MR 22 #3120; MR 28 #1326. H. Werner & R. Collinge, "Chebyshev approximations to the gamma function," Math. Comp., v. 15, 1961, p. 195.
- Erwin Madelung, Die mathematischen Hilfsmittel des Physikers, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band IV, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1950 (German). 4th ed. MR 0039021
Additional Information
- © Copyright 1966 American Mathematical Society
- Journal: Math. Comp. 20 (1966), 407-412
- MSC: Primary 65.25
- DOI: https://doi.org/10.1090/S0025-5718-1966-0202282-6
- MathSciNet review: 0202282