4 papers · 1 filter
Sharp Bounds for the Arc Lemniscate Sine Function
Horst Alzer, Man Kam Kwong
The arc lemniscate sine function is given by $$ \mbox{arcsl}(x)=\int_0^x \frac{1}{\sqrt{1-t^4}}dt. $$ In 2017, Mahmoud and Agarwal presented bounds for $\mbox{arcsl}$ in terms of t…
Identities involving Bernoulli and Euler polynomials
Horst Alzer, Semyon Yakubovich
We present various identities involving the classical Bernoulli and Euler polynomials. Among others, we prove that $$ \sum_{k=0}^{[n/4]}(-1)^k {n\choose 4k}\frac{B_{n-4k}(z) }{2^{6…
A Refinement of Vietoris Inequality for Cosine Polynomials
Horst Alzer, Man Kam Kwong
The classical Vietoris cosine inequality is refined by establishing a positive polynomial lower bound.
A Hardy-Littlewood Integral Inequality on Finite Intervals with a Concave Weight
Horst Alzer, Man Kam Kwong
A Hardy-Littlewood integral inequality on finite intervals with a concave weight is established. Given a function f on an interval [a,b], it is shown that the square of the weighte…