Derangements and applications.
Equations and inequalities involving .
Approximation of by .
Approximation of the dilogarithm function.
Inequalities on the Lambert function and hyperpower function.
Remarks on Ramanujan's inequality concerning the prime counting function
In this paper we investigate Ramanujan’s inequality concerning the prime counting function, asserting that for sufficiently large. First, we study its sharpness by giving full asymptotic expansions of its left and right hand sides expressions. Then, we discuss the structure of Ramanujan’s inequality, by replacing the factor on its right hand side by the factor for a given , and by replacing the numerical factor by a given positive . Finally, we introduce and study inequalities analogous...
Some results on derangement polynomials
We study moments of the difference concerning derangement polynomials . For the first moment, we obtain an explicit formula in terms of the exponential integral function and we show that it is always negative for . For the higher moments, we obtain a multiple integral representation of the order of the moment under computation.
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