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Summation of trigonometric series by Fourier transforms

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Abstract

This paper gives the theorems concerning the summation of trigonometric series with the help of Fourier transforms. By means of the known results of Fourier transforms, many difficult and complex problems of summation of trigonometric series can be solved. This method is a comparatively unusual way to find the summation of trigonometric series, and has been used to establish the comprehensive table of summation of trigonometric series. In this table 10 thousand series are given and most of them are new.

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References

  1. Harry, F. Davis,Fourier Series and Orthogonal Functions, Allyn and Bacon, Boston (1963).

    Google Scholar 

  2. Erdelyi, A., W. Magnus, F. Oberhettinger and F. G. Tricomi,Table of Integral Transformations, 2 vols., MacGraw Hill, New York (1950).

    Google Scholar 

  3. Oberhettinger, F.,Tables of Fourier Transformation, Springer (1957).

  4. Magnus, W., F. Oberhettinger, and R. P. Soni,Formulas and Theorems for the Special Functions of Mathematical Physics, Springer Verlag Berlin Heidelberg, New York (1966).

    Google Scholar 

  5. Stakgold, I.,Green's Functions and Boundary Value Problems, John Wiley and Sons, New York (1979).

    Google Scholar 

  6. Infeld, L., V.G. Smith and W. Z. Chien, On some series of Bessel functions,Journal of Mathematics and Physics, USA26, 1 (1947), 22–28.

    Google Scholar 

  7. Willers, Fr. A.,Practical Analysis, Dover (1948).

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University of Technology, Shanghai

    Chien Wei-zang

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  1. Chien Wei-zang
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Wei-zang, C. Summation of trigonometric series by Fourier transforms. Appl Math Mech 10, 385–397 (1989). https://doi.org/10.1007/BF02019228

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  • DOI: https://doi.org/10.1007/BF02019228

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