Fast computation of incomplete elliptic integral of first kind by half argument transformation

DOI10.1007/s00211-010-0321-8zbMath1201.65035OpenAlexW2056093739MaRDI QIDQ711585

Toshio Fukushima

Publication date: 27 October 2010

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-010-0321-8

zbMATH Keywords

algorithmnumerical examplesJacobian elliptic functionsincomplete elliptic integralBulirsch' functionCarlson's functionhalf argument formulas

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Elliptic functions and integrals (33E05) Numerical approximation and evaluation of special functions (33F05)

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Numerical analysis of periodic solutions and bifurcations in the planetary annulus problem ⋮ Dynamics of a particle under the gravitational potential of a massive annulus: properties and equilibrium description ⋮ Precise and fast computation of a general incomplete elliptic integral of third kind by half and double argument transformations ⋮ Precise and fast computation of Jacobian elliptic functions by conditional duplication ⋮ Recursive computation of derivatives of elliptic functions and of incomplete elliptic integrals ⋮ Precise computation of acceleration due to uniform ring or disk ⋮ Fast computation of a general complete elliptic integral of third kind by half and double argument transformations ⋮ Series expansions of symmetric elliptic integrals ⋮ Precise and fast computation of the general complete elliptic integral of the second kind ⋮ Precise and fast computation of a general incomplete elliptic integral of second kind by half and double argument transformations

Uses Software

• Mathematica
• NSWC
• algorithm 577
• efg

Cites Work

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• On the Series Expansion Method for Computing Incomplete Elliptic Integrals of the First and Second Kinds
• New Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kind

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