منابع مشابه
Fourier Series of Orthogonal Polynomials
It follows from Bateman [4] page 213 after setting = 1 2 . It can also be found with slight modi cation in Bateman [5] page122. However we are not aware of any reference where explicit formulas for the Fourier coef cients for Gegenbauer, Jacobi, Laguerre and Hermite polynomials can be found. In this article we use known formulas for the connection coef cients relating an arbitrary orthogonal po...
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Let m be a finite positive Borel measure supported in 1⁄2 1; 1 and introduce the discrete Sobolev type inner product
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For a family of weight functions that include the general Jacobi weight functions as special cases, exact condition for the convergence of the Fourier orthogonal series in the weighted L space is given. The result is then used to establish a Marcinkiewicz-Zygmund type inequality and to study weighted mean convergence of various interpolating polynomials based on the zeros of the corresponding o...
متن کاملFormulas for the Fourier Series of Orthogonal Polynomials in Terms of Special Functions
An explicit formula for the Fourier coef cients of the Legendre polynomials can be found in the Bateman Manuscript Project. However, formulas for more general classes of orthogonal polynomials do not appear to have been worked out. Here we derive explicit formulas for the Fourier series of Gegenbauer, Jacobi, Laguerre and Hermite polynomials. The methods described here apply in principle to an...
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By observing the equivalence of assertions on determining the jump of a function by its differentiated or integrated Fourier series, we generalize a previous result of Kvernadze, Hagstrom and Shapiro to the whole class of functions of harmonic bounded variation. This is achieved without the finiteness assumption on the number of discontinuities. Two results on determination of ...
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ژورنال
عنوان ژورنال: National Mathematics Magazine
سال: 1942
ISSN: 1539-5588
DOI: 10.2307/3028153