Anomalous Convergence of a Continued Fraction for Ratios of Kummer Functions

DOI10.2307/2006129zbMath0373.33002OpenAlexW4235076506MaRDI QIDQ4150546

Walter Gautschi

Publication date: 1977

Full work available at URL: https://doi.org/10.2307/2006129

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Classical hypergeometric functions, ({}_2F_1) (33C05) Convergence and divergence of continued fractions (40A15)

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On the Computation of Modified Bessel Function Ratios, Continued fractions associated with trigonometric and other strong moment problems, Continued fractions in numerical analysis, On the mathematical nature of Guseinov's rearranged one-range addition theorems for Slater-type functions, Computation of poles of two-point Padé approximants and their limits, Precise Coulomb wave functions for a wide range of complex \(\ell , \eta \) and \(z\), Coulomb and Bessel functions of complex arguments and order, Bibliography on the evaluation of numerical software, Two-point Padé expansions for a family of analytic functions, Transitory minimal solutions of hypergeometric recursions and pseudoconvergence of associated continued fractions, Truncation error bounds for limit-periodic continued fractions \(K(a_ n/1)\) with \(\lim a_ n=0\), On the computation of incomplete gamma functions in the complex domain, On bounds for Kummer’s function ratio

Cites Work

• Analysis of truncation error of approximations based on the Padé table and continued fractions
• A Computational Procedure for Incomplete Gamma Functions
• On the Computation of Modified Bessel Function Ratios
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