Description The n-th order derivative or integral of a function defined in a given range [a,b] is calculated through Fourier series expansion, where n is any real number and not necessarily integer. The necessary integrations are performed with the Gauss-Legendre quadrature rule. Selection for the number of desired Fourier coefficient pairs is made as well as for the number of the Gauss-Legendre integration points. Unlike many publicly available functions, the Gauss integration points k can be calculated for k>=46. The algorithm does not rely on the build-in Matlab routine roots to determine the roots of the Legendre polynomial, but finds the roots by looking for the eigenvalues of an alternative version of the companion matrix of the k th degree Legendre polynomial. The companion matrix is constructed as a symmetrical matrix, guaranteeing that all the eigenvalues (roots) will be real. On the contrary, the roots function us

FRACTIONAL_DIFFERINTEGRAL\cubic_polynomial_differintegral.m
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.........................\....\identity_function_differintegral.html
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