Some Identities on the q-Bernoulli Numbers and Polynomials with Weight 0 by T. Kim, J. Choi, Y. H. Kim

“…In this paper, we consider the q-Bernoulli numbers and polynomials with weight α=0 and give p-adic q-integral representation of Bernstein polynomials associated with q-Bernoulli numbers and polynomials with weight 0. …”
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Solving change of basis from Bernstein to Chebyshev polynomials by D.A. Wolfram

“…We provide two closed-form solutions to the change of basis from Bernstein polynomials to shifted Chebyshev polynomials of the fourth kind and show them to be equivalent by applying Zeilberger’s algorithm. …”
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Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis by Mohsen Alipour, Dumitru Baleanu, Fereshteh Babaei

“…We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. …”
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Approximation of the semi-infinite interval by A. McD. Mercer

“…The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. …”
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Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices by Mohsen Alipour, Dumitru Baleanu

“…Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the Bernstein polynomials (BPs). In the first method, we use the operational matrix of Caputo fractional derivative (OMCFD), and in the second one, we apply the operational matrix of Riemann-Liouville fractional integral (OMRLFI). …”
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Numerical Methods Based on the Hybrid Shifted Orthonormal Polynomials and Block-Pulse Functions for Solving a System of Fractional Differential Equations by Abdulqawi A. M. Rageh, Adel R. Hadhoud

“…This paper develops two numerical methods for solving a system of fractional differential equations based on hybrid shifted orthonormal Bernstein polynomials with generalized block-pulse functions (HSOBBPFs) and hybrid shifted orthonormal Legendre polynomials with generalized block-pulse functions (HSOLBPFs). …”
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Bernstein Collocation Method for Solving MHD Jeffery–Hamel Blood Flow Problem with Error Estimations by Ahmad Sami Bataineh, Osman Rasit Isik, Ishak Hashim

“…As a consequence, the solution is estimated using a numerical approach based on Bernstein polynomials, and the findings are verified by the 4th-order Runge–Kutta results. …”
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A New Spectral Mittag-Leffler Weighted Method to Solve Variable Order Fractional Differential Equations by Abdulrazzaq T. Abed, Ekhlass S. Al-Rawi

“…In addition, the effect of polynomials (such as Chebyshev, Jacobi, Legendre, Gegenbauer, Hermite, Taylor, Mittag-Leffler, and Bernstein polynomials) on the accuracy of the approximate solution is studied, and their effect was found to be minimal in most tests. …”
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