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Volume 7, Issue 2, Article 67 |
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An Inequality for Chebyshev Connection Coefficients
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Authors: |
James Guyker, |
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Keywords:
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Chebyshev coefficient, Ultraspherical polynomial, Polynomial expansion. |
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Date Received:
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19/01/06 |
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Date Accepted:
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11/03/06 |
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Subject Codes: |
41A50, 42A05, 42A32.
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Editors: |
Doru Stefanescu, |
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Abstract: |
Equivalent conditions are given for the nonnegativity of the coefficients of both the Chebyshev expansions and inversions of the first n polynomials defined by a certain recursion relation. Consequences include sufficient conditions for the coefficients to be positive, bounds on the derivatives of the polynomials, and rates of uniform convergence for the polynomial expansions of power series.
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