A transform involving Chebyshev polynomials and its inversion formula
نویسندگان
چکیده
منابع مشابه
An approximate method for Abel inversion using Chebyshev polynomials
Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone-beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel’s type integral equation. In this paper, a new stable algorithm based on shifted Chebyshev polynomial approxima...
متن کاملInversion Formulas Involving Orthogonal Polynomials and Some of Their Applications
We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special symmetric generalizations of the Hermite polynomials.
متن کاملA Fast, Simple, and Stable Chebyshev-Legendre Transform Using an Asymptotic Formula
A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(logN)2/ log logN) operations is derived. The basis of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the di...
متن کاملChebyshev Polynomials and Primality Tests
Algebraic properties of Chebyshev polynomials are presented. The complete factorization of Chebyshev polynomials of the rst kind (Tn(x)) and second kind (Un(x)) over the integers are linked directly to divisors of n and n + 1 respectively. For any odd integer n, it is shown that the polynomial Tn(x)=x is irreducible over the integers i n is prime. The result leads to a generalization of Fermat'...
متن کاملTotal Characters and Chebyshev Polynomials
The total character τ of a finite group G is defined as the sum of all the irreducible characters of G. K. W. Johnson asks when it is possible to express τ as a polynomial with integer coefficients in a single irreducible character. In this paper, we give a complete answer to Johnson’s question for all finite dihedral groups. In particular, we show that, when such a polynomial exists, it is uni...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2006
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.10.028