Sentence examples for large argument from inspiring English sources

However, the large argument approximation remains the same.

Examples of such problems are Bessel functions of large argument and large-order and doubly periodic functions.

Our method is especially powerful for the calculation of Riemann zeta function at large argument, while for smaller ones, it can also reach spectacular accuracies such as more than ten decimal places.

Since J 0 z) for large argument z is just cosine (J 0 z) ~ cos z − π/4)), the model (4) should have at least order 2 for the case of strong cyclicity.

Indeed, this follows from Corollary 2.2, the estimate (J_s(x)sim x^{s/2}), valid for small x (cf. e.g. 9.1.10 in in Abramowitz and Stegun [1]) and the standard asymptotic expansion begin{aligned} J_s(x)= sqrt{frac{2}{pi x}}cos (x-spi /2-pi /4)+O(x^{-1}) end{aligned}of the Bessel function of a large argument (cf. e.g. 9.2.1 in Abramowitz and Stegun [1]).

Using the large argument expansion of the error function complement [41] operatorname {erfc} z) simfrac{e^{-z^{2}}}{sqrt{pi}z} biggl 1-frac {1}{2z^{2}} biggl 1-fracmbox{1}{2z^{2}infty, (42) we observe that f(x) simgamma biggl(frac{1}{sqrt{pi x}} - frac{1}{sqrt{pi x}} biggr(1 - frac{1}{2gamma^{2} x} biggr) biggr), since (squaddelta} mbox{as{Sh}simgamma) as (mathit {Sh}gg1).

Therefore, in integral (3.11), we could replace the Bessel functions by their asymptotic at large arguments.

Thus, the function ψ is linear for small and moderate arguments, but increases more slowly than the liner one for large arguments.

On the other hand, for large arguments satisfying |e i, W 0)| > Δs, the weighting term in (8) decreases monotonously with the argument absolute value and, as a consequence, reduces the influence of outliers.

Since the calculations involve the evaluation of Euler's gamma function for large arguments, the result is approximate and the distribution is normalized only in the region of small values of d c.

But defenders of Israel cite its democratic status not to defend any particular behaviors, but rather as part of a larger argument for Westerners, primarily, to see Israel as largely sharing their values, and thus being worth defending, in general.