Olver, F. W. J.; Sookne, D. J. Note on backward recurrence algorithms. (English) Zbl 0261.65080 Math. Comput. 26, 941-947 (1972). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 17 Documents MSC: 65Q05 Numerical methods for functional equations (MSC2000) 65D20 Computation of special functions and constants, construction of tables 15A06 Linear equations (linear algebraic aspects) 33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\) 39A10 Additive difference equations 40A25 Approximation to limiting values (summation of series, etc.) 65G50 Roundoff error PDFBibTeX XMLCite \textit{F. W. J. Olver} and \textit{D. J. Sookne}, Math. Comput. 26, 941--947 (1972; Zbl 0261.65080) Full Text: DOI Digital Library of Mathematical Functions: §10.74(iv) Recurrence Relations ‣ §10.74 Methods of Computation ‣ Computation ‣ Chapter 10 Bessel Functions §3.6(v) Olver’s Algorithm ‣ §3.6 Linear Difference Equations ‣ Areas ‣ Chapter 3 Numerical Methods References: [1] Walter Gautschi, Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24 – 82. · Zbl 0168.15004 · doi:10.1137/1009002 [2] British Association for the Advancement of Science, “Bessel functions. Part II,” Mathematical Tables, v. 10, Cambridge University Press, Cambridge, 1952. · JFM 63.1144.03 [3] 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 [4] John G. Wills, On the use of recursion relations in the numerical evaluation of spherical Bessel functions and Coulomb functions, J. Computational Phys. 8 (1971), 162 – 166. · Zbl 0219.65019 [5] F. W. J. Olver, Bounds for the solutions of second-order linear difference equations, J. Res. Nat. Bur. Standards Sect. B 71B (1967), 161 – 166. · Zbl 0178.09702 [6] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. · Zbl 0063.08184 [7] W. Kahan, “Note on bounds for generating Bessel functions by recurrence.” (Unpublished.) [8] D. Jordan, Argonne National Laboratory Library Routine, ANL C370S–BESJY, October 1967. [9] Saburo Makinouchi, Note on the recurrence techniques for the calculation of Bessel functions \?\?(\?), Tech. Rep. Osaka Univ. 16 (1965), 185 – 201. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.