Related papers: On an infinite series for $(1+1/x)^x$
In this note, we present new properties for a sequence arising in some refinements of Carleman's inequality. Our results extend some results of Yang [Approximations for constant e and their applications J. Math. Anal. Appl. 262 (2001)…
In this paper, using the Maclaurin series of the functions $(1+x)^{1/x}$, some inequalities from papers Bicheng Debnath [1998] and Mortici Jang [2015] are generalized. For arbitrary Maclaurin series some general limits of Keller's type are…
We present inequalities and some applications to Kellers' limit and Carlemans' inequality.
The function $g(x)= (1+1/x)^{x}$ has the well-known limit $e$ as $x\rightarrow{\infty}$. The coefficients $c_{j}$ in an asymptotic expansion for $g(x)$ are considered. A simple recursion formula is derived, and then using Cauchy's integral…
The aim of this paper is to establish new inequalities for the Euler-Mascheroni by the continued fraction method.
Motivated by several generalizations of the well--known Mathieu series, the main object of this paper is to introduce new extension of generalized Mathieu series and to derive various integral representations of such series. Finally master…
It is well known that the Taylor series expansion of $(1+ z)^{A}$ does not converge for $|z|>1$ where A is a real number which is not equal to zero or a positive integer. A limited series expansion of this expression is obtained in this…
In this article it is proven the existence of integration of indefinite integrals as infinite derivative's series expansion. This also opens a new way to integrate a definite integral.
We improve constants in the Rademacher-Menchov inequality.
The aim of this work is to expose some asymptotic series associated to some expressions involving the volume of the n-dimensional unit ball. All proofs and the methods used for improving the classical inequalities announced in the final…
The aim of the present paper is to give extensions of the cosine-sine functional equation.
Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.
A new series expansion for the function (arctan(x)/x)^n is developed and some properties of the expansion coefficients are obtained.
In this paper, we are interested by the cotangent sum c0(q/p) related to the Estermann zeta function for the special case when q = 1 and get explicit formula for its series expansion, which represents an improvement of the identity (2:1)…
We obtain an improvement of the John-Nirenberg inequality for the series of the form $\sum_{n=1}^{\infty}n^{-1}e^{2\pi i n^k x},\;k>2,$ on intervals consisting of points of a same convergent of their continued fractions. We also establish a…
This paper considers some infinite series involving the Riemann zeta function.
We study finite sections of weighted Carleman's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant.
This is a survey, which is a continuation of the previous survey of the author about applications of Carleman estimates to Inverse Problems, J. Inverse and Ill-Posed Problems, 21, 477-560, 2013. It is shown here that Tikhonov functionals…
This paper is devoted to a generalization of a Hadamard type inequality for the permanent of a complex square matrix. Our proof is based on a non-trivial extension of a technique used in Carlen, Lieb and Loss (Methods and Applications of…
We prove a one-parameter family of sharp integral inequalities for functions on the $n$-dimensional unit ball. The inequalities are conformally invariant, and the sharp constants are attained for functions that are equivalent to a constant…