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On the -norm of Gegenbauer polynomials
1Graz University of Technology Institute of Analysis and Number Theory, Kopernikusgasse 24/II, 8010 Graz, Austria.
Mathematical Sciences : Quarterly Journal
|June 13, 2022
Summary
Gegenbauer polynomials, also called ultra-spherical polynomials, are useful in numerical analysis. This study derives a recursive formula and analyzes the asymptotic behavior of their norms.
Area of Science:
- Numerical Analysis
- Approximation Theory
Background:
- Gegenbauer polynomials, also known as ultra-spherical polynomials, are significant in various mathematical fields.
- Their applications are prevalent in numerical analysis and interpolation techniques.
Purpose of the Study:
- To derive a novel recursive formula for Gegenbauer polynomials.
- To compute and analyze the asymptotic behavior of the norm of Gegenbauer polynomials.
Main Methods:
- Derivation of a recursive formula specific to Gegenbauer polynomials.
- Asymptotic analysis techniques to determine the behavior of the polynomial norm.
Main Results:
- A new recursive formula for Gegenbauer polynomials has been established.
- The asymptotic behavior of the -norm for these polynomials has been successfully computed.
Conclusions:
- The findings provide valuable tools for numerical analysis and interpolation involving Gegenbauer polynomials.
- Understanding the asymptotic norm behavior enhances theoretical and practical applications.
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