The paper introduces Rational Kolmogorov-Arnold Networks (rKANs), a novel approach to function approximation using rational functions as basis functions. rKANs are an extension of traditional Kolmogorov-Arnold Networks (KANs) that initially used B-spline curves but faced implementation challenges due to their complexity. The authors explore two main approaches: Padé approximation and rational Jacobi functions. These methods are designed to enhance the accuracy and flexibility of KANs, particularly in handling functions with asymptotic behavior and singularities. The paper begins by reviewing Jacobi polynomials and their properties, including their orthogonality and the ability to be mapped to different domains. The authors then detail the construction of rKANs using these polynomials, with the first approach involving Padé approximation and the second using rational mappings. Both methods are evaluated through various deep learning tasks, including regression, classification, and physics-informed deep learning, such as solving differential equations. The experiments demonstrate that rKANs outperform traditional KANs and other methods in terms of accuracy and efficiency. However, the Padé-rKAN approach is noted to increase training time due to the computation of weighted polynomials. The paper concludes by suggesting future research directions, including the exploration of rational B-spline curves and further evaluation of fractional rational KANs for physics-informed problems.The paper introduces Rational Kolmogorov-Arnold Networks (rKANs), a novel approach to function approximation using rational functions as basis functions. rKANs are an extension of traditional Kolmogorov-Arnold Networks (KANs) that initially used B-spline curves but faced implementation challenges due to their complexity. The authors explore two main approaches: Padé approximation and rational Jacobi functions. These methods are designed to enhance the accuracy and flexibility of KANs, particularly in handling functions with asymptotic behavior and singularities. The paper begins by reviewing Jacobi polynomials and their properties, including their orthogonality and the ability to be mapped to different domains. The authors then detail the construction of rKANs using these polynomials, with the first approach involving Padé approximation and the second using rational mappings. Both methods are evaluated through various deep learning tasks, including regression, classification, and physics-informed deep learning, such as solving differential equations. The experiments demonstrate that rKANs outperform traditional KANs and other methods in terms of accuracy and efficiency. However, the Padé-rKAN approach is noted to increase training time due to the computation of weighted polynomials. The paper concludes by suggesting future research directions, including the exploration of rational B-spline curves and further evaluation of fractional rational KANs for physics-informed problems.