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Calculation of the modified Bessel functions of the second kind with complex argument. (English) Zbl 0143.17902


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[1] Irene A. Stegun and Milton Abramowitz, Generation of Bessel functions on high speed computers, Math. Tables Aids Comput 11 (1957), 255 – 257. · Zbl 0084.12101
[2] M. Goldstein and R. M. Thaler, Recurrence techniques for the calculation of Bessel functions, Math. Tables Aids Comput. 13 (1959), 102 – 108. · Zbl 0092.33002
[3] C. W. Clenshaw, Chebyshev series for mathematical functions, National Physical Laboratory Mathematical Tables, Vol. 5. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London, 1962. · Zbl 0114.07101
[4] E. E. Allen, Analytical approximations, Math. Tables and Other Aids to Computation 8 (1954), 240 – 241.
[5] 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. · Zbl 0078.12607
[6] Jet Wimp, Polynomial expansions of Bessel functions and some associated functions, Math. Comp. 16 (1962), 446 – 458. · Zbl 0109.29801
[7] F. D. Burgoyne, Polynomial approximations to \?\(_{0}\)(\?), \?\(_{1}\)(\?) and related functions, Math. Comp. 16 (1962), 497 – 498. · Zbl 0109.09903
[8] Henry E. Fettis, Numerical calculation of certain definite integrals by Poisson’s summation formula, Math. Tables Aids Comput. 9 (1955), 85 – 92. · Zbl 0066.10601
[9] Yudell L. Luke, Simple formulas for the evaluation of some higher transcendental functions, J. Math. and Phys. 34 (1956), 298 – 307. · Zbl 0070.12805
[10] D. B. Hunter, The calculation of certain Bessel functions, Math. Comp. 18 (1964), 123 – 128. · Zbl 0126.32202
[11] Wilhelm Magnus and Fritz Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1943 (German). · Zbl 0028.22102
[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. · Zbl 0099.11901
[14] 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. · Zbl 0036.24203
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