A Non-Linear Transcendental Formulation Converging Quadratically to the Golden Ratio using Pi and Euler-Mascheroni constant.

This paper introduces a closed-form transcendental formulation that converges quadratically to the Golden Ratio. The formulation is constructed by embedding a cosine recurrence relation initialized by a high-precision real seed bridging the square root of 𝜋 and the Euler-Mascheroni constant.