Counting methods of area integrals and Tchebychev polynomials of second
 kind on the ellipse

Q: What type of study is this?

This is a Quantitative Study study.

Abdelhamid Rehouma

doi:10.48550/arxiv.2506.00663

May 31, 2025Open Access

Counting methods of area integrals and Tchebychev polynomials of second kind on the ellipse

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Key Points

The study finds areas of circles, ellipses, and lemniscates using Gronwall's area formula.
Key metric includes using series expansions to compute areas from conformal mappings for precise results.
This analysis employs Laurent and Taylor series, indicating their importance in mapping techniques for area calculation.
The findings highlight the significance of orthogonal Tchebychev polynomials on the ellipse in mathematical interpolation.

Implication

This analysis computes areas using Gronwall's formula and explores Tchebychev polynomials' properties on ellipses.

Abstract

We use Gronwall's area formula to find the area of some differents regions as circles, ellipses and lemniscates.We use Laurent and Taylor series expansions of conformal mapping from the exterior of the unit disk to either of these regions to compute the area of them.We close this work with the discussion of orthogonal Tchebychev polynomials of second kind on the ellipse and interpolation.

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Cite This Study

Abdelhamid Rehouma (2025) studied this question.

synapsesocial.com/papers/68e6f342f8145af55aeaca8a https://doi.org/10.48550/arxiv.2506.00663

View Full Paper

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Counting methods of area integrals and Tchebychev polynomials of second kind on the ellipse

Key Points

Implication

Abstract

Discussion

Cite This Study

Counting methods of area integrals and Tchebychev polynomials of second kind on the ellipse

Key Points

Implication

Abstract

Discussion

Cite This Study

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