A New Reverse Extended Hardy–Hilbert’s Inequality with Two Partial Sums and Parameters

On a New Reverse Hilbert\'s Type Inequality

In this paper, by using the Euler-Maclaurin expansion for the Riemann-$zeta$ function, we establish an inequality of a weight coefficient. Using this inequality, we derive a new reverse Hilbert's type inequality. As an applications, an equivalent form is obtained.

A hybrid mean value involving a new Gauss sums and Dedekind sums

‎In this paper‎, ‎we introduce a new sum‎ ‎analogous to Gauss sum‎, ‎then we use the properties of the‎ ‎classical Gauss sums and analytic method to study the hybrid mean‎ ‎value problem involving this new sums and Dedekind sums‎, ‎and‎ ‎give an interesting identity for it.

Partial Sums of Two Quartic q-Series

X iv :0 90 4. 34 53 v1 [ m at h. C A ] 2 2 A pr 2 00 9 Symmetry, Integrability and Geometry: Methods and Applications SIGMA 5 (2009), 050, 19 pages Partial Sums of Two Quartic q-Series Wenchang CHU † and Chenying WANG ‡ † Dipartimento di Matematica, Università degli Studi di Salento, Lecce-Arnesano P. O. Box 193, Lecce 73100, Italy E-mail: [email protected] ‡ College of Mathematics and Phys...

Lévy’s inequality, Rademacher sums, and Kahane’s inequality

Let (Ω,A , P ) be a probability space. A random variable is a Borel measurable function Ω→ R. For a random variable X, we denote by X∗P the pushforward measure of P by X. X∗P is a Borel probability measure on R, called the distribution of X. A random variable X is called symmetric when the distribution of X is equal to the distribution of −X. Because the collection {(−∞, a] : a ∈ R} generates t...

A New Half-discrete Mulholland-type Inequality with Parameters