The coefficients of differentiated expansions and derivatives of ultraspherical polynomials
نویسندگان
چکیده
منابع مشابه
The 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...
متن کاملthe 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...
متن کاملOn Rapid Computation of Expansions in Ultraspherical Polynomials
We present an O(N log2 N) algorithm for the computation of the first N coefficients in the expansion of an analytic function in ultraspherical polynomials. We first represent expansion coefficients as an infinite linear combination of derivatives and then as an integral transform with a hypergeometric kernel along the boundary of a Bernstein ellipse. Following a transformation of the kernel, we...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1991
ISSN: 0898-1221
DOI: 10.1016/0898-1221(91)90089-m