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Sampling Theorem Based Fourier–Legendre Transform

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Abstract

The product of any number of Legendre functions, under a restricted domain, can be expanded by the corresponding Legendre polynomials, with the coefficient being the sinc function. While an analogous expansion can be made for any number of Gengenbauer functions, it is not allowed for more than two Jacobi functions. To obtain such an expansion, the sampling theorem is of great availability.

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Acknowledgements

The authors are indebted to T. Kobayashi and H. Fujisaka for stimulating discussions and suggestions.

Funding

Funding was provide by Hiroshima City University.

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Authors and Affiliations

  1. Graduate School of Information Sciences, Hiroshima City University, Asaminami-ku, Hiroshima, 731-3194, Japan

    S. Kuwata

  2. Department of System Engineering, Hiroshima City University, Asaminami-ku, Hiroshima, 731-3194, Japan

    K. Kawaguchi

Authors
  1. S. Kuwata
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  2. K. Kawaguchi
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Correspondence to S. Kuwata.

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Kuwata, S., Kawaguchi, K. Sampling Theorem Based Fourier–Legendre Transform. Int. J. Appl. Comput. Math 6, 89 (2020). https://doi.org/10.1007/s40819-020-00844-z

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  • DOI: https://doi.org/10.1007/s40819-020-00844-z

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