Merovci, Faton Power product inequalities for the \(\Gamma_k \) function. (English) Zbl 1207.33001 Int. J. Math. Anal., Ruse 4, No. 21-24, 1007-1012 (2010). Summary: We give an upper and a lower power product estimate for the \(k\)-gamma function\[ \begin{split} \frac{k^nn!}{(x)_{n,k}}\cdot \bigg(\frac{x_kn}{k+kn}\bigg)^{kn}\cdot e^{[\frac1k H(n)-1](x-k)}\leq \Gamma_k(x)\leq \frac{k^{n+1}(n+1)!}{(x)_{n+1,k}}\cdot \bigg(\frac{x_kn}{k+kn}\bigg)^{kn}\cdot e^{[\frac1k H(n+1)-1](x-k)}\\ (x>0,\;k>0,\;n=1,2,\dots) \end{split} \]hold, where \(H(n)=1+\frac12+\cdots+\frac1n\). Cited in 11 Documents MSC: 33B15 Gamma, beta and polygamma functions 26D07 Inequalities involving other types of functions Keywords:\(\Gamma _k\) function; inequalities PDFBibTeX XMLCite \textit{F. Merovci}, Int. J. Math. Anal., Ruse 4, No. 21--24, 1007--1012 (2010; Zbl 1207.33001) Full Text: Link