Khan, Nabiullah Usman, Talha Aman, Mohd Al-Omari, Shrideh Araci, Serkan
Published in
Advances in Difference Equations

The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright functions, expressed in terms of the generalized Wright hypergeometric function and in terms of the generalized hypergeometric function as well. Based on the main results, some integral formulas involving different special functions c...

Qi, Feng Guo, Bai-Ni

In the paper, the authors review origins, motivations, and generalizations of a series of inequalities involving several exponential functions and sums, establish three new inequalities involving finite exponential functions and sums by finding convexity of a function related to the generating function of the Bernoulli numbers, survey the history, ...

Ghosh, Surajit

Riemann hypothesis stands proved in three different ways.To prove Riemann hypothesis from the functional equation concept of Delta function and projective harmonic conjugate of both Gamma and Delta functions are introduced similar to Gamma and Pi function. Other two proofs are derived using Eulers formula and elementary algebra. Analytically contin...

Cerf, Raphaël Dembin, Barbara

We consider the anchored isoperimetric profile of the infinite open cluster, defined for p > p_c, whose existence has been recently proved in [3]. We extend adequately the definition for p = p_c, in finite boxes. We prove a partial result which implies that, if the limit defining the anchored isoperimetric profile at pc exists, it has to vanish.

Ibrahim, Rabha W.
Published in
SN Applied Sciences

Reducing noise from images is an essential structure of the image processing study. Noises can arise with images through achievement on diffusion. The existence of noise can delay the right operation of these images for many applications such as satellite and medical images. Reducing denois in images multiplicatively (DIM) has been developed and mo...

prodanov, dimiter

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represen...

prodanov, dimiter

This paper establishes a real integral representation of the reciprocal Gamma function in terms of a regularized hypersingular integral along the real line. A regularized complex representation along the Hankel path is derived. The equivalence with the Heine&rsquo / s complex representation is demonstrated. For both real and complex integrals, the ...

Campbell, John

Recently, there have been a variety of intriguing discoveries regarding the symbolic computation of series containing central binomial coefficients and harmonic-type numbers. In this article, we present a vast generalization of the recently-discovered harmonic summation formula $$\sum_{n=1}^{\infty} \binom{2n}{n}^{2} \frac{H_{n}}{32^{n}} = \frac{\G...

Hasan, Md. Mahmudul Foad, Mohammad Mahadi Hasan
Published in
Circuits, Systems, and Signal Processing

Orthogonal frequency division multiplexing is a special form of multicarrier modulation and suffers from a very high peak-to-average power ratio (PAPR) that degrades overall performance of the system. In this article, a modified gamma correction companding (MGCC) is proposed that provides a significant reduction in PAPR when compared with existing ...

Li, Xi-Qiao Liu, Zhi-Ming Yang, Zhen-Hang Zheng, Shen-Zhou
Published in
Journal of Inequalities and Applications

Among various approximation formulas for the gamma function, Smith showed that Γ(x+12)∼S(x)=2π(xe)x(2xtanh12x)x/2,x→∞,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \...