On the L2-norm of Gegenbauer polynomials

Damir Ferizović

doi:10.1007/s40096-021-00398-1

On the L2-norm of Gegenbauer polynomials

Titel in Übersetzung: Über die L2-Norm der Gegenbauer Polynome

Damir Ferizović

Institut für Analysis und Zahlentheorie (5010)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

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.

Titel in Übersetzung	Über die L2-Norm der Gegenbauer Polynome
Originalsprache	englisch
Seitenumfang	5
Fachzeitschrift	Mathematical Sciences
Jahrgang	15
DOIs	https://doi.org/10.1007/s40096-021-00398-1
Publikationsstatus	Veröffentlicht - 2021

ASJC Scopus subject areas

Analyse
Angewandte Mathematik
Numerische Mathematik
Statistik und Wahrscheinlichkeit
Information systems
Signalverarbeitung
Angewandte Informatik

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10.1007/s40096-021-00398-1

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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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N2 - 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.

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KW - Asymptotics

KW - Gegenbauer polynomials

KW - L-norm

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DO - 10.1007/s40096-021-00398-1

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On the L2-norm of Gegenbauer polynomials

Abstract

ASJC Scopus subject areas

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