  This paper presents a comprehensive survey of 18 distinct polynomials and
their potential applications in Kolmogorov-Arnold Network (KAN) models as an
alternative to traditional spline-based methods. The polynomials are classified
into various groups based on their mathematical properties, such as orthogonal
polynomials, hypergeometric polynomials, q-polynomials, Fibonacci-related
polynomials, combinatorial polynomials, and number-theoretic polynomials. The
study aims to investigate the suitability of these polynomials as basis
functions in KAN models for complex tasks like handwritten digit classification
on the MNIST dataset. The performance metrics of the KAN models, including
overall accuracy, Kappa, and F1 score, are evaluated and compared. The
Gottlieb-KAN model achieves the highest performance across all metrics,
suggesting its potential as a suitable choice for the given task. However,
further analysis and tuning of these polynomials on more complex datasets are
necessary to fully understand their capabilities in KAN models. The source code
for the implementation of these KAN models is available at
https://github.com/seydi1370/Basis_Functions .
