Some Properties of the Fuss–Catalan Numbers

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.

Keywords

• Fuss–Catalan number
• Catalan–Qi function
• Catalan number
• monotonicity
• logarithmic convexity
• complete monotonicity
• minimality
• inequality