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

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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.

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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