6 citations · 6 across the 8 of their papers we have counts for
11 papers
Inequalities for 1/(1-cos(x)) and its derivatives
Horst Alzer, Henrik L. Pedersen
We prove that the function is completely monotonic on and absolutely monotonic on , and we determine the best possible bounds…
Inequalities for trigonometric sums
Horst Alzer, Man Kam Kwong
We present several new inequalities for trigonometric sums. Among others, we show that the inequality $$ \sum_{k=1}^n (n-k+1)(n-k+2)k\sin(kx) > \frac{2}{9} \sin(x) \bigl( 1+2\cos(x…
Identities for combinatorial sums involving trigonometric functions
Horst Alzer, Semyon Yakubovich
Let and $$ B_{m,n}(a)=\sum_{j=0}^m (-4)^j {m+j+1\choose 2j+1}\sum_{k=0}^{n-1}…
On a combinatorial identity of Chaundy and Bullard
Horst Alzer, Omran Kouba
We give two new proofs of the Chaundy-Bullard formula and we prove the "twin formula…
Inequalities for Taylor series involving the divisor function
Horst Alzer, Man Kam Kwong
Let where denotes the number of positive divisors of the natural number . We present monotonicity properties of functi…
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…
On a Sine Polynomial of Turan
Horst Alzer, Man Kam Kwong
In 1935, P. Turán proved that We present various related inequalities. Among others, w…
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…
Sturm Theorem and a Refinement of Vietoris Inequality for Cosine Polynomials
Horst Alzer, Man Kam Kwong
In a recent work, the authors established a refinement of the well-known 1958 result of Vietoris on nonnegative cosine polynomials. In four places of the proof, use was made of the…