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Calculation of the modified Bessel functions of the second kind with complex argument


Author: Fr. Mechel
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
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  • [1] I. A. Stegun & M. Abramowitz, "Generation of Bessel functions on high speed computers," MTAC, v. 11, 1957, pp. 255-257. MR 20 #459. MR 0093939 (20:459)
  • [2] M. Goldstein & R. M. Thaler, "Recurrence techniques for the calculation of Bessel functions," MTAC, v. 13, 1959, pp. 102-108. MR 21 #4530. MR 0105794 (21:4530)
  • [3] C. W. Clenshaw, Chebyshev Series for Mathematical Functions, Nat. Phys. Lab. Math. Tables, Vol. 5, Dept. Scientific and Indust. Research, Her Majesty's Stationery Office, London, 1962. MR 26 #362. MR 0142793 (26:362)
  • [4] C. Hastings, Jr. & J. P. Wong, Jr., "Analytical approximations," MTAC, v. 8, 1954, p. 46. MR 0064483 (16:289c)
  • [5] A. J. M. Hitchcock, "Polynomial approximations to Bessel functions of order zero and one and to related functions," MTAC, v. 11, 1957, pp. 86-188. MR 19, 64. MR 0085598 (19:64b)
  • [6] J. Wimp, "Polynomial expansions of Bessel functions and some associated functions," Math. Comp., v. 16, 1902, pp. 446-458. MR 26 #6452. MR 0148956 (26:6452)
  • [7] F. D. Burgoyne, "Polynomial approximations to $ {I_0}(x)$, $ {I_1}(x)$ and related functions," Math. Comp., v. 16, 1962, pp. 497-498. MR 26 #5196. MR 0147682 (26:5196)
  • [8] H. E. Fettis, "Numerical calculation of certain definite integrals by Poisson's summation formula," MTAC, v. 9, 1955, pp. 85-92. MR 17, 302. MR 0072546 (17:302f)
  • [9] Y. L. Luke, "Simple formulas for the evaluation of some higher transcendental functions," J. Math. Phys., v. 34, 1956, pp. 298-307. MR 17, 1138. MR 0078047 (17:1138e)
  • [10] D. B. Hunter, "The calculation of certain Bessel functions," Math. Comp., v. 18, 1964, pp. 123-128. MR 28 #1330. MR 0158104 (28:1330)
  • [11] Wilhelm Magnus & Fritz Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer, Berlin, 1943; 2nd ed., 1948; English transl., Chelsea, New York, 1949. MR 9, 183, MR 10, 38, 532. MR 0022272 (9:183b)
  • [12] 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.
  • [13] H. Werner & R. Collinge, "Chebyshev approximations to the gamma function," Math. Comp., v. 15, 1961, p. 195.
  • [14] E. Madelung, Die mathematischen Hilfsmittel des Physikers, 4th ed., Die Grundlehren der mathematischen Wissenschaften, Bd. 4, Springer, Berlin, 1950; 7th ed., 1964, p. 69. MR 12, 484. MR 29 #1773. MR 0039021 (12:484g)

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DOI: https://doi.org/10.1090/S0025-5718-1966-0202282-6
Article copyright: © Copyright 1966 American Mathematical Society

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