This paper introduces orthogonal polynomials into the framework of Kolmogorov-Arnold Networks (KANs) by replacing spline parameterized edges with two variants: (1) discrete Shmaliy polynomials and (2) the classical Legendre polynomials, while keeping nodes as input summation points. We evaluate these polynomial-based networks against the original spline-based KAN across three benchmarks. On Fashion MNIST, Shmaliy reaches 87.6% accuracy while Legendre achieves 88.3% (KAN: 87.3%). For chest X-ray pneumonia detection, Shmaliy achieves 93.1% while Legendre matches KAN’s 95.0%. For OrganAMNIST CT scan classification, Legendre attains 96.2%, outperforming both Shmaliy (89.3%) and KAN (94.5%). The results demonstrate that Legendre polynomials match or exceed KAN performance, while Shmaliy remains competitive. This establishes orthogonal polynomials as both viable alternatives to splines in KAN architectures and a promising direction for neural network design, particularly for medical imaging tasks where Legendre polynomials show significant advantages.