Inequalities play a fundamental role in both theoretical and applied mathematics contain many patterns of symmetries. In studies, inequalities have been used to provide estimates some functions based on the properties their symmetry. this paper, we present following new asymptotic expansion related ordinary gamma function ?(1+w)?2?w(w/e)ww2+760w2?120w/2exp?r=1??rwr,w??, with recurrence relation...

In this paper, for $1<p<\infty$, we obtain the $L^p$-boundedness of Hilbert transform $H^{\gamma}$ along a variable plane curve $(t,u(x_1, x_2)\gamma(t))$, where $u$ is Lipschitz function with small norm, and $\gamma$ general satisfying some suitable smoothness curvature conditions.

Using the Bernstein theorem we give a simple proof of complete monotonicity three parameter generalized Mittag-Leffler function $E_{\alpha, \beta}^{\gamma}(-x)$ for $x \geq 0$ and suitably adjusted parameters $\alpha$, $\beta$ $\gamma$