An upper bound on Jacobi polynomials

Authors:
Ilia Krasikov
Affiliations:
Department of Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, UK
Venue:
Journal of Approximation Theory
Year:
2007

Citing 5
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Abstract

Let P"k^(^@a^,^@b^)(x) be an orthonormal Jacobi polynomial of degree k. We will establish the following inequality:maxx@?[@d"-"1,@d"1](x-@d"-"1)(@d"1-x)(1-x)^@a(1+x)^@bP"k^(^@a^,^@b^)(x)^2=6,@a=@b=1+24.