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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally we will use these results to state several relations for Gegenbauer polynomials.
📌 3 Key Takeaways
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Objective & Hypothesis:We generalize the first and second kind Chebyshev polynomials by using the concepts and the operational formalism of the Hermite polynomials of the Kampé de Fériet type.
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Key Findings & Data:We will see how it is possible to derive integral representations for these generalized Chebyshev polynomials.
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Conclusion & Impact:Finally we will use these results to state several relations for Gegenbauer polynomials.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Two-variable Chebyshev and Gegenbauer polynomials · Generating functions · Integral representations
Abstract
We generalize the first and second kind Chebyshev polynomials by using the concepts and the operational formalism of the Hermite polynomials of the Kampé de Fériet type. We will see how it is possible to derive integral representations for these generalized Chebyshev polynomials. Finally we will use these results to state several relations for Gegenbauer polynomials.
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Cite This Article
Cesarano, C. (2014). Generalized Chebyshev polynomials. Hacettepe Journal of Mathematics and Statistics, Volume: 43 Issue: 5. https://ajindex.com/articles/1403364