On the L2-norm of Gegenbauer polynomials

Damir Ferizović

doi:10.1007/s40096-021-00398-1

On the L2-norm of Gegenbauer polynomials

Damir Ferizović

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

Gegenbauer, also known as ultra-spherical, polynomials appear often in numerical analysis or interpolation. In the present text we find a recursive formula for and compute the asymptotic behavior of their L²-norm.

Translated title of the contribution	Über die L2-Norm der Gegenbauer Polynome
Original language	English
Number of pages	5
Journal	Mathematical Sciences
Volume	15
DOIs	https://doi.org/10.1007/s40096-021-00398-1
Publication status	Published - 2021

Keywords

Asymptotics
Gegenbauer polynomials
L-norm

ASJC Scopus subject areas

Analysis
Applied Mathematics
Numerical Analysis
Statistics and Probability
Information Systems
Signal Processing
Computer Science Applications

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10.1007/s40096-021-00398-1

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title = "On the L2-norm of Gegenbauer polynomials",

abstract = "Gegenbauer, also known as ultra-spherical, polynomials appear often in numerical analysis or interpolation. In the present text we find a recursive formula for and compute the asymptotic behavior of their L2-norm.",

keywords = "Asymptotics, Gegenbauer polynomials, L-norm",

author = "Damir Ferizovi{\'c}",

note = "Funding Information: The author thankfully acknowledges support by the Austrian Science Fund (FWF): F5503 “Quasi-Monte Carlo Methods” and FWF: W1230 “Doctoral School Discrete Mathematics,” and the Austrian Marshall Plan Foundation. Publisher Copyright: {\textcopyright} 2021, The Author(s).",

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N1 - Funding Information: The author thankfully acknowledges support by the Austrian Science Fund (FWF): F5503 “Quasi-Monte Carlo Methods” and FWF: W1230 “Doctoral School Discrete Mathematics,” and the Austrian Marshall Plan Foundation. Publisher Copyright: © 2021, The Author(s).

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KW - Asymptotics

KW - Gegenbauer polynomials

KW - L-norm

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SN - 2008-1359

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JO - Mathematical Sciences

JF - Mathematical Sciences

ER -

On the L2-norm of Gegenbauer polynomials

Abstract

Keywords

ASJC Scopus subject areas

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