The Erdélyi--Magnus--Nevai and Krasikov Conjectures for Jacobi Polynomials

What the math gives to ML

The paper proves a sharp, degree- and parameter-sensitive envelope for weighted orthonormal Jacobi polynomials, including the non-removable intermediate growth factor S^{1/3}. This can be transferred to neural networks as a principled bounded polynomial feature basis: instead of feeding raw high-degree Jacobi polynomials into an MLP, use endpoint-weighted functions with theorem-based degree normalization. The bound provides an explicit scale for coefficient initialization and regularization, potentially enabling higher-degree polynomial layers with fewer activation and gradient explosions.