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• W2797765693 abstract "The Catalan numbers, the generalized Catalan numbers, the Fuss numbers, and the Fuss–Catalan numbers are integer sequences, which have a long history, are of combinatorial interpretations, and have been attracting combinatorialists and number theorists. Since April 2015, the authors, their coauthors, and other mathematicians generalized analytically the Catalan numbers, the generalized Catalan numbers, the Fuss numbers, and the Fuss–Catalan numbers to the Catalan–Qi function, the q -Catalan–Qi numbers, and the Fuss–Catalan–Qi function respectively and discovered some new properties of the Catalan numbers, the Catalan function, the generalized Catalan numbers, the Fuss numbers, the Catalan–Qi numbers, the q -Catalan–Qi numbers, the Catalan–Qi function, the Fuss–Catalan numbers, and the Fuss–Catalan–Qi function. These properties include explicit expressions, asymptotic expansions, monotonicity, logarithmic convexity, (logarithmically) complete monotonicity, minimality, Schur-convexity, product inequalities, determinantal inequalities, exponential representations, integral representations, generating functions, connections with the Bessel polynomials and the Bell polynomials of the second kind, identities, inequalities, product-ratio expressions, supercongruences, and so on. In the expository chapter, the authors review and survey the above-mentioned analytic generalizations and properties of the Catalan numbers, the generalized Catalan numbers, the Fuss numbers, the Fuss–Catalan numbers, the Catalan function, the Catalan–Qi function, the q -Catalan–Qi numbers, and the Fuss–Catalan–Qi function." @default.
• W2797765693 created "2018-04-24" @default.
• W2797765693 creator A5046693977 @default.
• W2797765693 creator A5073122046 @default.
• W2797765693 date "2018-04-10" @default.
• W2797765693 modified "2023-10-12" @default.
• W2797765693 title "Some Properties and Generalizations of the Catalan, Fuss, and Fuss-Catalan Numbers" @default.
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• W2797765693 doi "https://doi.org/10.1002/9781119414421.ch5" @default.
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