University of Guilan Journal of Mathematical Modeling 2345-394X 10 3 2022 09 01 An improved upper bound for ultraspherical coefficients 421 431 5370 10.22124/jmm.2022.21255.1861 EN Mehdi Hamzehnejad Department of Mathematics, Faculty of Science and Modern Technology, Graduate University of Advanced Technology, Kerman, Iran Mohammad Mehdi Hosseini Department of Applied Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran Abbas Salemi Department of Applied Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran Journal Article 2021 12 07 In this paper, new upper bounds for the ultraspherical coefficients of differentiable functions are presented. Using partial sums of ultraspherical polynomials, error approximations are presented to estimate differentiable functions. Also, an error estimate of the Gauss-Jacobi quadrature is obtained and we state an upper bound for Legendre coefficients which is sharper than upper bounds proposed so far. Numerical examples are given to assess the efficiency of the presented theoretical results. Ultraspherical coefficients approximation error upper bound Gauss-Jacobi quadrature https://jmm.guilan.ac.ir/article_5370_367adbf16f4af4cbcb7aa9540c34c1d0.pdf