Research Paper (undergraduate) from the year 2026 in the subject Didactics - Physics, , language: English, abstract: This paper derives a novel force formula from a relativistic Lagrangian incorporating gamma functions and inverse tangent terms, yielding F = (2 m_0 a / p) tan^{-1} [ (p / 2) (1 + a^2 / c^2)^n G(1 + a/ ) / G(1 - a/ ) ]. Unlike standard special relativity's divergent ^3 m_0 a, this expression saturates at high energies, modeling bounded interactions in quark-gluon plasmas or metamaterials. Derivation from action principles ensures Lorentz covariance. Limits recover Newtonian mechanics and cap ultra-relativistic forces. Numerical examples and comparisons demonstrate 15-25% deviations in TeV regimes, suggesting applications in particle accelerators and nonlinear field theories.

Professor Dr. Fazal Rehman is a distinguished mathematician and researcher from Pakistan. He is widely known for introducing innovative mathematical principles and original formulas. In 2013, he presented the Rehman's Concentric Octagram, a novel approach related to the value of p. He has developed numerous rules for sums of consecutive even and odd numbers. Dr. Fazal Rehman is also recognized for creative techniques in number theory and algebra. His work emphasizes simplification, mental mathematics, and mathematical beauty. He has collaborated internationally with researchers from Bhutan and Pakistan. Several alternate formulations of classical theorems are credited to his name. He actively contributes to mathematical research, writing, and education. Professor Dr. Fazal Rehman continues to inspire students through original thinking in mathematics.