Transitory minimal solutions of hypergeometric recursions and pseudoconvergence of associated continued fractions

DOI10.1090/S0025-5718-07-01934-5zbMath1110.33001OpenAlexW2127529702MaRDI QIDQ3426027

Alfredo Deaño, Javier Segura

Publication date: 7 March 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-01934-5

zbMATH Keywords

hypergeometric functionscontinued fractionsrecurrence relationscondition and stabilitynumerical evolution of special functions

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Continued fractions; complex-analytic aspects (30B70) Classical hypergeometric functions, ({}_2F_1) (33C05) Convergence and divergence of continued fractions (40A15) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

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A generalized inverse trinomial distribution with application ⋮ Numerical methods for the computation of the confluent and Gauss hypergeometric functions ⋮ Numerically satisfactory solutions of Kummer recurrence relations ⋮ A three-term recurrence relation for accurate evaluation of transition probabilities of the simple birth-and-death process ⋮ Computational properties of three-term recurrence relations for Kummer functions ⋮ Numerically satisfactory solutions of hypergeometric recursions

Cites Work

• The numerical computation of the confluent hypergeometric function U(a,b,z)
• Numerically satisfactory solutions of hypergeometric recursions
• Anomalous Convergence of a Continued Fraction for Ratios of Kummer Functions
• Numerical Methods for Special Functions
• Computational Aspects of Three-Term Recurrence Relations
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