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The research aims to find analytical simplifications for incomplete elliptic integrals using mathematical modeling techniques.

March 17, 2026Open Access

Analytical Simplification of Incomplete Elliptic Integrals of the First Kind: Continued Fraction Modeling via Symmetric Substitution and Padé Approximants

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The research aims to find analytical simplifications for incomplete elliptic integrals using mathematical modeling techniques.
Utilized continued fraction modeling to represent elliptical integrals.
Applied symmetric substitution to improve accuracy in representations.
Employed Padé approximants for better approximation of functions.
Demonstrated effective simplifications for calculating incomplete elliptic integrals.
Achieved higher accuracy compared to traditional methods.
Provided a more efficient computational strategy for elliptic integrals.

Analytical simplification reveals efficient continued fraction models for incomplete elliptic integrals, indicating enhanced computation methods.

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SungKun Kim (2026) studied this question.

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Analytical simplification reveals efficient continued fraction models for incomplete elliptic integrals, indicating enhanced computation methods.