High-precision computation of the confluent hypergeometric functions via Franklin-Friedman expansion
DOI10.1007/S10444-017-9565-5zbMath1393.33008OpenAlexW2759554388MaRDI QIDQ723741
Publication date: 24 July 2018
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10444-017-9565-5
confluent hypergeometric functionsarbitrary-precision arithmeticFranklin-Friedman expansionuniform series expansion
Symbolic computation and algebraic computation (68W30) Computation of special functions and constants, construction of tables (65D20) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Numerical approximation and evaluation of special functions (33F05)
Uses Software
Cites Work
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- Mellin transforms and asymptotics: Finite differences and Rice's integrals
- Fast and accurate algorithm for the generalized exponential integral \(E_{\nu}(x)\) for positive real order
- Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions
- Computing the Kummer function \(U\)(\textit{a, b, z}) for small values of the arguments
- Hyperasymptotic solutions of second-order linear differential equations. I
- The evaluation of Bessel functions via exp-arc integrals
- High-precision evaluation of the Bessel functions via Hadamard series
- Asymptotic Methods for Integrals
- UNIFORM ASYMPTOTIC EXPANSIONS OF LAPLACE INTEGRALS
- Effective Laguerre Asymptotics
- Laplace type integrals: transformation to standard form and uniform asymptotic expansions
- Uniform, Exponentially Improved, Asymptotic Expansions for the Confluent Hypergeometric Function and Other Integral Transforms
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