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Three Improvements in Reduction and Computation of Elliptic Integrals
1Ames Laboratory and Department of Mathematics, Iowa State University, Ames, IA 50011-3020.
Summary
This study simplifies elliptic integral reduction formulas and introduces a faster computation series for elliptic integrals of the third kind. These advancements improve the efficiency and applicability of elliptic integral calculations in mathematics and physics.
Area of Science:
- Mathematics
- Numerical Analysis
- Computational Physics
Background:
- Elliptic integrals are fundamental in various scientific fields.
- Existing methods for reduction and computation can be computationally intensive.
- Simplification and faster algorithms are needed for broader applications.
Purpose of the Study:
- To improve the reduction and computation of elliptic integrals.
- To present a more efficient series for numerical computation.
- To provide a series expansion in elementary symmetric functions.
Main Methods:
- Modification of intermediate "basic integrals" for simplified reduction formulas.
- Development of a faster than quadratically convergent series for numerical computation.
- Derivation of a series expansion in elementary symmetric functions.
Main Results:
- Simplified reduction formulas for elliptic integrals.
- A novel, efficient series for the complete symmetric elliptic integral of the third kind.
- Series expansion coefficients provided for the symmetric elliptic integral of the first kind up to degree seven.
Conclusions:
- The proposed methods offer significant improvements in the reduction and computation of elliptic integrals.
- The new series provide enhanced efficiency for numerical calculations.
- The series expansion is a valuable tool for analyzing elliptic and hyperelliptic integrals.
Keywords:
computational algorithmelementary symmetric functionelliptic integralhyperelliptic integralhypergeometric R-functionrecurrence relationsseries expansionMore Related Videos
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