منابع مشابه
On the denseness of Jacobi polynomials
Let X represent either a space C[−1,1] or L α,β(w), 1 ≤ p < ∞, of functions on [−1,1]. It is well known that X are Banach spaces under the sup and the p-norms, respectively. We prove that there exist the best possible normalized Banach subspaces Xα,β of X such that the system of Jacobi polynomials is densely spread on these, or, in other words, each f ∈ Xα,β can be represented by a linear combi...
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One of the interesting features in the development of analysis in the twentieth century is the remarkable growth, in various directions, of the theory of orthogonal functions. Two brilliant achievements on the threshold of this century—Fejér's paper on Fourier series and Fredholm's papers on integral equations—have been acting as a powerful inspiring source of attraction, inviting analysts to d...
متن کاملOn linearization coefficients of Jacobi polynomials
This article deals with the problem of finding closed analytical formulae for generalized linearization coefficients for Jacobi polynomials. By considering some special cases we obtain a reduction formula using for this purpose symbolic computation, in particular Zeilberger’s and Petkovsek’s algorithms.
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15 صفحه اولThe coefficients of differentiated expansions of double and triple Jacobi polynomials
Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. Extension to expansion of triple Jacobi polynomials is given. The results for the special cases of double and triple ultraspher...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2004
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171204305314