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Integer Powers of Arcsin

Author

Listed:
  • Jonathan M. Borwein
  • Marc Chamberland

Abstract

New simple nested-sum representations for powers of the arcsin function are given. This generalization of Ramanujan's work makes connections to finite binomial sums and polylogarithms.

Suggested Citation

  • Jonathan M. Borwein & Marc Chamberland, 2007. "Integer Powers of Arcsin," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-10, May.
    • Handle: RePEc:hin:jijmms:019381
    DOI: 10.1155/2007/19381
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    Cited by:

    1. Chunli Li & Wenchang Chu, 2024. "Generating Functions for Binomial Series Involving Harmonic-like Numbers," Mathematics, MDPI, vol. 12(17), pages 1-15, August.
    2. Joseph Tonien, 2024. "Fibonacci-Related Formulas for Pi," The Mathematical Intelligencer, Springer, vol. 46(3), pages 214-221, September.
    3. Ling Zhu, 2022. "The Natural Approaches of Shafer-Fink Inequality for Inverse Sine Function," Mathematics, MDPI, vol. 10(4), pages 1-8, February.
    4. Díaz, Mateo & Quiroz, Adolfo J. & Velasco, Mauricio, 2019. "Local angles and dimension estimation from data on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 229-247.
    5. Ling Zhu, 2022. "A Natural Approximation to the Complete Elliptic Integral of the First Kind," Mathematics, MDPI, vol. 10(9), pages 1-8, April.

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