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Polynomials and Trigonometric Polynomials

  • George Pólya
  • Gabor Szegö
Part of the Classics in Mathematics book series (CLASSICS)

Abstract

Setting cos ϑ = x, the expressions
$$ T_n \left( x \right) = \cos n\vartheta {\text{ }}U_n \left( x \right) = \frac{1} {{n + 1}}T'_{n + 1} \left( x \right) = \frac{{\sin \left( {n + 1} \right)\vartheta }} {{\sin \vartheta }}'{\text{ }}n = 0,1,2,... $$
are polynomials in x of degree n (the Tchebychev polynomials); the leading coefficient of T n (x) is equal to 2 n-1 and that of U n (x) is equal to 2 n , n = 1, 2, 3,....

Keywords

Legendre Polynomial Trigonometric Polynomial Equality Sign Basis Polynomial Real Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • George Pólya
    • 1
  • Gabor Szegö
    • 1
  1. 1.Stanford UniversityStanfordUSA

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