A modification of standard Poincaré asymptotic expansions for functions defined by means of Laplace transforms is analyzed. This modification is based on an alternative power series expansion of the integrand, and the convergence properties are seen to be superior to those of the original asymptotic series. The resulting modified asymptotic expansion involves confluent hypergeometric functions ...

In this paper, we present a new sharp approximation for the gamma function via the tri-gamma function. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are provided for demonstrating the superiority of our approximation.

We calculated numerically the values of L-functions of four typical elliptic curves in the critical strip in the range Im(s) ≤ 400. We found that all the non-trivial zeros in this range lie on the critical line Re(s) = 1 and are simple except the one at s = 1. The method we employed in this paper is the approximate functional equation with incomplete gamma functions in the coefficients. For inc...

We investigated the neural correlates of the perception of human goal-directed action by 8-month-old infants. Infants viewed video loops of complete and incomplete actions, which they could discriminate according to our pilot study, while we recorded their electrophysiological brain activity. Analysis of bursts of gamma-band oscillations resulting from passive viewing of these stimuli indicated...

Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^nsubseteqmathbb{C}^n$ given by $$Phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$  where $gammain[0,1/2]$, $z=(z_1,hat{z})in B^n$ and $$Psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$ in which $betain[0,1]$, $f(z_1)neq 0$ a...