A Note on $k$-Gamma Function and Pochhammer $k$-Symbol
Keywords:Factorial function, Pochhammer $k$-symbol, $k$-Gamma function
AbstractIn 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.
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