Abstract
This paper presents new results of Bernoulli polynomials. New derivative expressions of some celebrated orthogonal polynomials and other polynomials are given in terms of Bernoulli polynomials. Hence, some new connection formulas between these polynomials and Bernoulli polynomials are also deduced. The linking coefficients involve hypergeometric functions of different arguments that can be summed in some cases. Formulas that express some celebrated numbers in terms of Bernoulli numbers are displayed. Based on the new connection formulas between different polynomials and Bernoulli polynomials, along with some well-known integrals involving these polynomials, new closed forms for some definite integrals are given.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference41 articles.
1. Shen, J., Tang, T., and Wang, L.L. Spectral Methods: Algorithms, Analysis and Applications, 2011. Volume 41.
2. Boyd, J. Chebyshev and Fourier Spectral Methods, 2001.
3. Hesthaven, J.S., Gottlieb, S., and Gottlieb, D. Spectral Methods for Time-Dependent Problems, 2007. Volume 21.
4. Numerical solution method for multi-term variable order fractional differential equations by shifted Chebyshev polynomials of the third kind;Polata;Alex. Eng. J.,2022
5. Tau and Galerkin operational matrices of derivatives for treating singular and Emden–Fowler third-order-type equations;Abd-Elhameed;Int. J. Mod. Phys.,2022
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