Uniform inequalities for Gegenbauer polynomials
Copyright policy )Uniform inequalities for Gegenbauer polynomials
The usual asymptotic representations of the Gegenbauer (ultraspherical) polynomials do not yield bounds on their absolute values which hold equally on the interval \(-1\leq x\leq 1\). But in the Legendre case (index \(\lambda= {1\over 2}\)) and more generally in the case of \(0\leq \lambda\leq 1\) such estimates exist. In this paper such bounds are given explicitly for arbitrary \(\lambda>0\).
- TU Dortmund University Germany
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), inequalities for Gegenbauer polynomials, Basic spherical functions, spherical harmonics (continuous and discrete)
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), inequalities for Gegenbauer polynomials, Basic spherical functions, spherical harmonics (continuous and discrete)
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