Deformed Newton's $(s,t)$-Binomial Series and Generating Functions of Generalized Central Binomial Coefficients and Generalized Catalan Numbers

Ronald Orozco L\'opez

Deformed Newton's $(s,t)$-Binomial Series and Generating Functions of Generalized Central Binomial Coefficients and Generalized Catalan Numbers

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arxiv 2306.07431 v3 pith:23JF4GUA submitted 2023-06-12 math.GM

Ronald Orozco López This is my paper

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keywords binomialgeneralizeddeformedcatalancentralcoefficientsfunctionsgenerating

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abstract

We define the deformed $(s,t)$-binomial formula and the deformed Newton $(s,t)$-binomial series, and we will use it to establish the generating functions of the generalized central binomial coefficients and the generalized Catalan numbers.

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Cited by 1 Pith paper

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Deformed Bivariate $q$-Appell Polynomials
math.CO 2025-05 reject novelty 5.0 of 10

This work introduces deformed bivariate q-Appell polynomials and derives many structural formulas, but a key characterization theorem contains an error that propagates into the examples.

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