Computation of modified Bessel functions and their ratios. (English) Zbl 0277.65006


65D20 Computation of special functions and constants, construction of tables
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
41-04 Software, source code, etc. for problems pertaining to approximations and expansions
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[1] Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. · Zbl 0171.38503
[2] D. E. Amos, Bounds on iterated coerror functions and their ratios, Math. Comp. 27 (1973), 413 – 427. · Zbl 0288.33004
[3] D. E. Amos, Evaluation of Some Cumulative Distribution Functions by Numerical Quadrature, Symposium Proceedings, Sixth Annual Symposium of Interface: Computer Science and Statistics, University of California, Berkeley, October 16-17, 1972.
[4] 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
[5] C. W. Clenshaw and Susan M. Picken, Chebyshev series for Bessel functions of fractional order, National Physical Laboratory Mathematical Tables, Vol. 8, Her Majesty’s Stationery Office, London, 1966.
[6] Walter Gautschi, Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24 – 82. · Zbl 0168.15004
[7] Yudell L. Luke, On generating Bessel functions by use of the backward recurrence formula, Aerospace Research Laboratories, Air Force Systems Command, United States Air Force, Wright-Patterson Air Force Base, Ohio, 1972. ARL 72-0030. · Zbl 0234.33010
[8] Yudell L. Luke, Inequalities for generalized hypergeometric functions, J. Approximation Theory 5 (1972), 41 – 65. Collection of articles dedicated to J. L. Walsh on his 75th birthday, I. · Zbl 0225.33004
[9] Yudell L. Luke, The special functions and their approximations. Vol. II, Mathematics in Science and Engineering, Vol. 53, Academic Press, New York-London, 1969. · Zbl 0193.01701
[10] F. W. J. Olver, Numerical solution of second-order linear difference equations, J. Res. Nat. Bur. Standards Sect. B 71B (1967), 111 – 129. · Zbl 0171.36601
[11] F. W. J. Olver, Tables for Bessel functions of moderate or large orders, National Physical Laboratory Mathematical Tables, Vol. 6. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London, 1962. · Zbl 0112.36103
[12] F. W. J. Olver, The asymptotic expansion of Bessel functions of large order, Philos. Trans. Roy. Soc. London. Ser. A. 247 (1954), 328 – 368.
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