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Some Properties of the Fuss–Catalan Numbers

Author

Listed:
  • Feng Qi

    (Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
    College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia, China
    School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China)

  • Pietro Cerone

    (Department of Mathematics and Statistics, La Trobe University, Melbourne (Bundoora) 3086, Victoria, Australia)

Abstract

In the paper, the authors express the Fuss–Catalan numbers as several forms in terms of the Catalan–Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the Fuss–Catalan numbers, and derive a double inequality for bounding the Fuss–Catalan numbers.

Suggested Citation

  • Feng Qi & Pietro Cerone, 2018. "Some Properties of the Fuss–Catalan Numbers," Mathematics, MDPI, vol. 6(12), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:277-:d:185215
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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.

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