## Asymptotic behaviour of trigonometric series with modified monotone coefficients |

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### Contents

The Coefficients | 1 |

Convergence of The Series and Integrability | 38 |

Asymptotic Behaviour of fx and gx | 52 |

Copyright | |

1 other sections not shown

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2rcosx Aafc Abel transformation Adamovic Aljancic arbitrarily large assume the asymptotic assumption asymptotic behaviour asymptotic relation Bojanic and Karamata Bojanic and Tomic C. H. Yong Chap Chapter condition converges everywhere converges uniformly cosine series 1-1 cosnx denote Dirichlet Kernel diverges established theorems fc-i fc=i Fejer kernel finite interval Fourier coefficients Fourier series Hence implies Integrability theorems known results Lb(tk Lb(x Lemma III—4 logn measurable slowly varying monograph monotone coefficients monotone function monotone sequences monotone slowly varying n-l oo n^Lin observe oo oo positive measurable function Proof of Theorem prove the sufficiency prove Theorem proved that S(x Publications de L'Institut pure bounded variation quasi-monotone coefficients quasi-monotone sequence R. P. Boas Riemann integral satisfies series with quasi-monotone sine series 1-2 sinkx sinnx slowly varying functions Suppose Theorem III—10 Theorem III—36(i trigonometric series uniform convergence write