Catalan Numbers in Terms of $(\alpha, k)-$Gamma Function and $(\alpha, k)-$Beta Function

Year 2023, Volume: 15 Issue: 1, 164 - 170, 30.06.2023

Abdullah Akkurt , Huseyin Yıldırım

https://doi.org/10.47000/tjmcs.1182387

https://izlik.org/JA66DR26UF

Abstract

In the paper, the authors discuss some extended results involving the Catalan numbers and establish an integral representation of the Catalan numbers in terms of the $(\alpha,k)$-gamma and $(\alpha,k)$-beta function. We refer to the results available in the literature by giving special values to the parameters in the obtained theorems.

Keywords

Catalan number , $(\alpha,k)$-gamma function , $(\alpha,k)$-beta function

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