Computational Aspects of Three-Term Recurrence Relations

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Previous article Next article Computational Aspects of Three-Term Recurrence RelationsWalter GautschiWalter Gautschihttps://doi.org/10.1137/1009002PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] M. Abramowitz, Review 58, Math. Tables Aids Comput, 10 (1956), 176– Google Scholar[2] Renata Babušková, Über numerische Stabilität einiger Rekursionsformeln, Apl. Mat., 9 (1964), 186–193 MR0187365 0123.11104 Google Scholar[3] T. A. Bancroft, Some recurrence formulae in the incomplete beta function ratio, Ann. Math. Statistics, 20 (1949), 451–455 MR0030653 0041.03402 CrossrefISIGoogle Scholar[4] G. Blanch, Numerical evaluation of continued fractions, SIAM Rev., 6 (1964), 383–421 10.1137/1006092 MR0171374 0133.38904 LinkISIGoogle Scholar[5] British Association For The Advancement Of Science, Bessel functions. Part II. Functions of positive integer order, British Association for the Advancement of Science, Mathematical Tables, vol. X, University Press, Cambridge, 1952xl+255 MR0050973 0049.09409 Google Scholar[6] Herbert Buchholz, Die konfluente hypergeometrische Funktion mit besonderer Berücksichtigung ihrer Anwendungen, Ergebnisse der angewandten Mathematik. Bd. 2, Springer-Verlag, Berlin, 1953xvi+234 MR0054783 0050.07402 CrossrefGoogle Scholar[7] C. W. Clenshaw, The numerical solution of linear differential equations in Chebyshev series, Proc. Cambridge Philos. Soc., 53 (1957), 134–149 MR0082196 0077.32503 CrossrefGoogle Scholar[8] Lothar Collatz, The numerical treatment of differential equations. 3d ed, Translated from a supplemented version of the 2d German edition by P. G. Williams. Die Grundlehren der mathematischen Wissenschaften, Bd. 60, Springer-Verlag, Berlin, 1960xv+568 pp. (1 plate) MR0109436 0086.32601 CrossrefGoogle Scholar[9] F. J. Corbató, On the computation of auxiliary functions for two-center integrals by means of a high-speed computer, J. Chem. Phys., 24 (1956), 452–453 CrossrefGoogle Scholar[10] Fernando J. Corbató and , Jack L. Uretsky, Generation of spherical Bessel functions in digital computers, J. Assoc. Comput. Mach., 6 (1959), 366–375 MR0105792 0087.28104 CrossrefISIGoogle Scholar[11] A. Erdélyi, Asymptotic expansions, Dover Publications Inc., New York, 1956vi+108 MR0078494 0070.29002 Google Scholar[12] Arthur Erdélyi, , Wilhelm Magnus, , Fritz Oberhettinger and , Francesco G. Tricomi, Higher transcendental functions. Vol. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xxvi+302 MR0058756 0051.30303 Google Scholar[13] Arthur Erdélyi, , Wilhelm Magnus, , Fritz Oberhettinger and , Francesco G. Tricomi, Higher transcendental functions. Vol. II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xvii+396 MR0058756 0052.29502 Google Scholar[14] M. A. Efgrafov, A new proof of Perron's theorem, Izvestiya Akad. Nauk SSSR. Ser. Mat., 17 (1953), 77–82 MR0058109 Google Scholar[15] L. Fox, A short table for Bessel functions of integer orders and large arguments, Royal Society Shorter Mathematical Tables, No. 3, Cambridge, at the University Press, 1954, 28– MR0065245 0058.11402 Google Scholar[16] Walter Gautschi, Recursive computation of the repeated integrals of the error function, Math. Comp., 15 (1961), 227–232 MR0136074 0099.11401 Google Scholar[17] W. Gautschi, Algorithm 222—Incomplete beta function ratios, Comm. ACM, 7 (1964), 143–144, Certification of Algorithm 222, Ibid., p. 244 10.1145/363958.363967 CrossrefISIGoogle Scholar[18] W. Gautschi, Algorithm 236—Bessel functions of the first kind, Comm. ACM, 7 (1964), 479–480, Certification of Algorithm 236, Ibid., 8 (1965), pp. 105–106 10.1145/355586.355587 CrossrefISIGoogle Scholar[19] W. Gautschi, Algorithm 259—Legendre functions for arguments larger than one, Comm. ACM, 8 (1965), 488–492 10.1145/365474.355591 CrossrefISIGoogle Scholar[20] W. Gautschi, Algorithm 292—Regular Coulomb wave functions, Comm. ACM, 9 (1966), 793–795 10.1145/365876.365884 CrossrefISIGoogle Scholar[21] A. O. Gel'Fond, Calculus of Finite Differences, Gosud. Izdat. Fiz.-Mat. Lit., Moscow, 1959, (German and French translations of the first edition are available.) Google Scholar[22] M. Goldstein and , R. M. Thaler, Recurrence techniques for the calculation of Bessel functions, Math. Tables Aids Comput., 13 (1959), 102–108 MR0105794 0092.33002 CrossrefGoogle Scholar[23] Marion C. Gray, Bessel functions of integral order and complex argument, Comm. ACM, 4 (1961), 169– 10.1145/355578.366318 MR0151652 CrossrefISIGoogle Scholar[24] Philip Hartman, Ordinary differential equations, John Wiley & Sons Inc., New York, 1964xiv+612 MR0171038 0125.32102 Google Scholar[25] D. R. Hartree, Some properties and applications of the repeated integrals of the error function, Mem. Proc. Manchester Lit. Philos. Soc., 80 (1936), 85–102 Google Scholar[26] Sin Hitotumatu, Note on the computation of Bessel functions through recurrence formula, J. Math. Soc. Japan, 15 (1963), 353–359 MR0156008 0131.34401 CrossrefGoogle Scholar[27] C. W.