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Integral Representations of the Catalan Numbers and Their Applications

Author

Listed:
  • Feng Qi

    (Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan Province, China
    College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia Autonomous Region, China
    Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300387, China)

  • Bai-Ni Guo

    (School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, Henan Province, China)

Abstract

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

Suggested Citation

  • Feng Qi & Bai-Ni Guo, 2017. "Integral Representations of the Catalan Numbers and Their Applications," Mathematics, MDPI, vol. 5(3), pages 1-31, August.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:3:p:40-:d:106754
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    References listed on IDEAS

    as
    1. Qi, Feng & Mortici, Cristinel, 2015. "Some best approximation formulas and inequalities for the Wallis ratio," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 363-368.
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    Cited by:

    1. Jian Cao & Wen-Hui Li & Da-Wei Niu & Feng Qi & Jiao-Lian Zhao, 2023. "A Brief Survey and an Analytic Generalization of the Catalan Numbers and Their Integral Representations," Mathematics, MDPI, vol. 11(8), pages 1-16, April.
    2. Feng Qi & Xiao-Ting Shi & Bai-Ni Guo, 2018. "Integral Representations of the Large and Little Schröder Numbers," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(1), pages 23-38, March.
    3. Wathek Chammam, 2019. "Several formulas and identities related to Catalan-Qi and q-Catalan-Qi numbers," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 1039-1048, December.

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