Neven Elezovic

Learn More
The Hermite-Hadamard inequality is used to develop an approximation to the logarithm of the gamma function which is more accurate than the Stirling approximation and easier to derive. Then the concavity of the logarithm of gamma of logarithm is proved and applied to the Jensen inequality. Finally, the Wallis ratio is used to obtain the additional term in(More)
Let s , t be two given real numbers , s = t and m ∈ N. We determine the coefficients a j (s, t) in the asymptotic expansion of integral (or differential) mean of polygamma functions ψ (m) (x) : 1 t − s t s ψ (m) (x + u) d u ∼ ψ (m) x ∞ ∑ j=0 a j (s, t) x j , x → ∞. We derive the recursive relations for polynomials a j (t , s) , and also as polynomials in(More)
We give an overview of the use of asymptotic expansions of gamma and related functions — ratio of gamma functions, powers, digamma and polygamma functions. The aim is to introduce a general theory which can unify various particular formulas for factorial functions and binomial coefficients. The connection with inequalities for gamma function is established.(More)