arXiv subjects
Publications and source records attributed to József Sándor.
We evaluate some finite and infinite sums involving $q$-trigonometric and $q$-digamma functions. Upon letting $q$ approach $1$, one obtains corresponding sums for the classical trigonometric and the digamma functions. Our key argument is a theta product formula of Jacobi and Gosper's $q$-trigonometric identities.
We consider convexity and monotonicity properties for some functions related to the $q$-gamma function. As applications, we give a variety of inequalities for the $q$-gamma function, the $q$-digamma function $ψ_q(x)$, and the $q$-series. Among other consequences, we improve a result of Azler~and~Grinshpan about the zeros of the function $ψ_q(x)$. We use $q$-analogues for the Gauss multiplication formula to put in closed form members of some of our inequalities.
We give a new proof for a product formula of Jacobi which turns out to be equivalent to a $q$-trigonometric product which was stated without proof by Gosper. We apply this formula to derive a $q$-analogue for the Gauss multiplication formula for the gamma function. Furthermore, we give explicit formulas for short products of $q$-gamma functions.
In this paper, authors generalize logarithmic mean $L$, Neuman-Sándor $M$, two Seiffert means $P$ and $T$ as an application of generalized trigonometric and hyperbolic functions. Moreover, several two-sided inequalities involving these generalized means are established.
In this paper authors establish the two sided inequalities for the following two new means $$X=X(a,b)=Ae^{G/P-1},\quad Y=Y(a,b)=Ge^{L/A-1}.$$ As well as many other well known inequalities involving the identric mean $I$ and the logarithmic mean are refined from the literature as an application.
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
The aim of this paper is to prove new trigonometric and hyperbolic inequalities, which constitute among others refinements or analogs of famous Cusa-Huygens, Wu-Srivastava, and related inequalities. In most cases, the obtained results are sharp.
We study the exact extremal orders of compositions $f(g(n))$ of certain arithmetical functions, including the functions $σ(n)$, $ϕ(n)$, $σ^*(n)$ and $ϕ^*(n)$, representing the sum of divisors of $n$, Euler's function and their unitary analogues, respectively. Our results complete, generalize and refine known results.