Mathematical Physics

Evaluation of Elliptic Integrals Via the Comprehensive System of Functions: Elimination of Transcendental Non-Integrability

Authors: Vitaliy Boltian

This paper introduces a novel mathematical framework based on the Comprehensive System of Functions to evaluate classical elliptic integrals of the first, second, and third kinds. By mapping incomplete functional profiles directly onto complete trigonometric and hyperbolic invariants of the real system of functions, the traditional transcendental complexity and artificial limitations of non-integrability are completely eliminated. The proposed method provides exact analytical solutions in elementary functions, ensuring high numerical convergence and stabilizing the relative error within a strict range of 10u207bu2075 to 10u207bu2076 without requiring iterative numerical processing cycles."

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[v1] 2026-09-22 20:49:22

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