Some Formulas and Recurrences of Certain Orthogonal Polynomials Generalizing Chebyshev Polynomials of the Third-Kind

This paper investigates certain Jacobi polynomials that involve one parameter and generalize the well-known orthogonal called Chebyshev of third-kind. Some new formulas are developed for these polynomials. We will show some previous results in literature can be considered special ones our derived formulas. The derivatives moments derived. Hence, two important explicitly give terms their original deduced as cases. expressions different symmetric non-symmetric expressed combinations generalized third-kind linearization also given using approaches. appearing coefficients hypergeometric functions. Furthermore, several cases, existing functions summed standard or through employment suitable symbolic algebra, particular, Zeilberger’s algorithm.