Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Anomalous convergence of a continued fraction for ratios of Kummer functions


Author: Walter Gautschi
Journal: Math. Comp. 31 (1977), 994-999
MSC: Primary 30A22; Secondary 65B99
DOI: https://doi.org/10.1090/S0025-5718-1977-0442204-3
MathSciNet review: 0442204
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We exhibit a phenomenon of apparent convergence to the wrong limit in connection with a continued fraction of Perron for ratios of Kummer functions. The phenomenon is further illustrated in the special cases of Bessel functions and incomplete gamma functions.


References [Enhancements On Off] (What's this?)

  • [1] W. GAUTSCHI, "An evaluation procedure for incomplete gamma functions," ACM Trans. Mathematical Software. (To appear.) MR 547763 (81f:65015)
  • [2] W. GAUTSCHI & J. SLAVIK, "On the computation of modified Bessel function ratios," Math. Comp. (To appear.) MR 0470267 (57:10025)
  • [3] W. B. JONES, "Analysis of truncation error of approximations based on the Padé table and continued fractions," Rocky Mountain J. Math., v. 4, 1974, pp. 241-250. MR 49 #6551. MR 0341805 (49:6551)
  • [4] O. PERRON, Die Lehre von den Kettenbrüchen, Vol. II, 3rd ed., Teubner, Stuttgart, 1957. MR 19, 25. MR 0085349 (19:25c)
  • [5] L. J. SLATER, "Confluent hypergeometric functions," Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (M. Abramowitz & I. A. Stegun, Editors), Nat. Bur. Standards, Appl. Math. Ser., no. 55, Superintendent of Documents, U. S. Government Printing Office, Washington, D. C., 1964, pp. 503-535. MR 29 #4914. MR 0167642 (29:4914)
  • [6] H. S. WALL, Analytic Theory of Continued Fractions, Van Nostrand, New York, 1948; reprint, Chelsea, New York, 1967. MR 10, 32. MR 0025596 (10:32d)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 30A22, 65B99

Retrieve articles in all journals with MSC: 30A22, 65B99


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1977-0442204-3
Keywords: Continued fractions, apparent convergence to the wrong limit, Bessel functions, incomplete gamma functions
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society