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portada Compressed Chebyshev Polynomials and Multiple-Angle Formulas
Type
Physical Book
Author
Publisher
Language
English
Pages
52
Format
Paperback
Dimensions
22.9x15.2x0.3 cm
Weight
0.09 kg.
ISBN13
9786200624987
Categories

Compressed Chebyshev Polynomials and Multiple-Angle Formulas

Gerzson Kéri (Author) · Globeedit · Paperback

Compressed Chebyshev Polynomials and Multiple-Angle Formulas - Kéri, Gerzson

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Synopsis "Compressed Chebyshev Polynomials and Multiple-Angle Formulas"

This small book combines two themes. It starts with a survey on the mathematical solution methods for the cubic equation, where the solution with the Cardano's formula as well as the trigonometric and hyperbolic solution methods are explained and discussed for both the general and the canonical form of the cubic equation. The main theme is, however, the paradigm of multiple-angle formulas that can be expressed with the Chebyshev polynomials. By the compression of the Chebyshev polynomials, the multiple-angle formulas and later the factorization formulas become more elegant. The multiple-angle formulas form a bridge between the two themes, whereas the easy triple-angle cases of some of these formulas, namely the formulas for cos(3t), cosh(3t) and sinh(3t), are applied during the trigonometric and hyperbolic solution. From this fact springs the idea of considering and solving similar equations where the triple angles are extended to arbitrary multiple angles. In connection with an asymptotic analysis, a conjecture and another open problem are proposed to solve. Next we turn from continuous to discrete mathematics, namely divisibility rules and factorization.

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