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Unified solution for the Legendre equation in the interval [−1, 1]—An example of solving linear singular-ordinary differential equations

Author

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  • Zhang, Qing-Hua
  • Ma, Jian
  • Qu, Yuanyuan

Abstract

This study adopts the corrected Fourier series expansion method with only limited smooth degree to solve the Legendre equation with an arbitrary complex constant μ, and finds general solution for the intervals [0, 1] and [−1, 0], which includes a logarithm singular function in forms of ln(1−x) and ln(1+x), respectively, and a nonsingular function. The smooth conjunction of these two portions at x=0 constructs the unified solution for the Legendre equation in the interval [−1, 1].

Suggested Citation

  • Zhang, Qing-Hua & Ma, Jian & Qu, Yuanyuan, 2016. "Unified solution for the Legendre equation in the interval [−1, 1]—An example of solving linear singular-ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 311-323.
    • Handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:311-323
    DOI: 10.1016/j.amc.2016.05.028
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    Cited by:

    1. Qing-Hua Zhang & Jian Ma & Yuanyuan Qu, 2016. "Bessel Equation in the Semiunbounded Interval : Solving in the Neighbourhood of an Irregular Singular Point," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-7, July.

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