## Fourier series and orthogonal polynomials |

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### Contents

Definition of Fourier series | 1 |

Orthogonality of sines and cosines | 2 |

Determination of the coefficients | 3 |

Copyright | |

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### Common terms and phrases

approaches zero arbitrary function becomes infinite Bessel boundary value problem Chapter VII constant multiple continuous function convergence coordinates corresponding cos2 cosine sum Courant-Hilbert defined definition denoted derivative differential equation discussion equal expression finite jumps finite number Fourier series func function f(x function of period given graph harmonic polynomial Hermite polynomials hypothesis identity independent integral values integrand interval irn(x Jacobi polynomials Jn(x Jo(x kx dx Laguerre Laguerre polynomials Laplace series Laplace's equation left-hand member Legendre polynomials Legendre series linear combination Ln(x mathematical nomials non-negative normalized notation nth degree nth order obtained orthogonal polynomials paragraph partial sum particular period 2ir pk(x Pn(x poly positive roots power series property of orthogonality recurrence formula relation representation respect right-hand member rn(x sin2 sinh sn(x solution spherical harmonics substitution SUPPLEMENTARY REFERENCES theorem tion Tn(x trigonometric sum uniformly bounded vanishes weight function yn(x