A Note on $k$-Gamma Function and Pochhammer $k$-Symbol (Journal of Informatics and Mathematical Sciences, 2014)
In this note, we discuss some extended results involving the Pochhammer's symbol and express the multiple factorials in terms of the said symbol. We prove the $k$-analogue of Vandermonde's theorem which contains the binomial theorem as a limiting case. Also, we introduce some limit formulae involving the $k$-symbol and prove the $k$-analogue Gauss multiplication and Legendere's duplication theorems by using these formulae.
Keywords: Factorial function; Pochhammer $k$-symbol; $k$-Gamma function