Related papers: Some inequalities for the beta function and its ra…
In this paper we set up the theory of acid zeta function and ajoint acid zeta function, based on the theory, we point out a reason to doubt the truth of the Riemann hypothesis and also as a consequence, we give out some new RH equivalences.
The table of Gradshteyn and Ryzhik contains some integrals that can be expressed in terms of the incomplete beta function. We describe some elementary properties of this function and use them to check some of the formulas in the mentioned…
We present a new lower bound for Euler's beta function, $B(x,y)$, which states that the inequality \begin{equation*} B(x,y)>\frac{x+y}{xy}\left(1-\frac{2xy}{x+y+1}\right) \end{equation*} holds on $(0,1]\times(0,1]$, which improves a lower…
In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the…
In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality.
The purpose of this paper is to provide a random version of Simons' inequality.
We introduce the beta function of a knot in euclidean three-space. This is a meromorphic function of a complex variable which we prove admits a Bernstein type functional equation. We determine the first residues.
In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result in [\emph{Inequalities and…
The logarithmic convexity of restrictions of the Beta functions to rays parallel to the main diagonal and the functional equation \[ \phi\left( x+1\right) =\frac{x\left( x+k\right) }{\left( 2x+k+1\right) \left( 2x+k\right) }\phi\left(…
In this paper, we establish some new integral inequalities for $(\alpha, m)-$convex functions and quasi-convex functions, respectively. Our results in special cases recapture known results.
This note introduces a new range of modified gamma and beta $k$ functions. The authors present new modified gamma and beta $k$-functions, first and second summation relations, various functionals, Mellin transforms, and integral…
In this paper, additional properties of the lower gamma functions and the error functions are introduced and proven. In particular, we prove interesting relations between the error functions and Laplace transform.
The relation between the boolean functions and Bell inequalities for qubits is analyzed. The connection between the maximal quantum violation of a Bell inequality and the nonlinearity of the corresponding boolean function is discussed. A…
A new Hilbert-type integral inequality in the whole plane with the non-homogeneous kernel and parameters is given. The constant factor related to the hypergeometric function and the beta function is proved to be the best possible. As…
In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.
In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.
We prove in this note one weight norm inequalities for some positive Bergman-type operators.
We prove new Pitt inequalities for the Fourier transforms with radial and non-radial weights using weighted restriction inequalities for the Fourier transform on the sphere. We also prove new Riemann-Lebesgue estimates and versions of the…
We calculate some infinite sums containing the digamma function in closed-form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as…
In this study, we obtain some convexity, monotonicity and additivity properties as well as some inequalities involving the Nielsen's $\beta$-function which was introduced in 1906.