# Search Results

] Allasia , G. , Giordano , C. , Pečarić , J. 2002 Inequalities for the Gamma function relating to asymptotic expansions Math. Inequal. Appl. 5 543 – 555 . [3] Alzer , H. 2003

Let*T*
_{n}
*(x)* be trigonometric polynomial of degree*n*, and
be conjugation of*T*
_{n}
*(x)*. In this paper we obtain the complete asymptotic expansion for

*n*→∞.

## Abstract

The problem of the existence of an asymptotic expansion of type

*D*

^{n}. Particularly meaningful are several characterizations of the polynomial asymptotic expansions of an

*n*th order convex function.

## Abstract

Merging asymptotic expansions are established for the distribution functions of suitably centered and normed linear combinations
of winnings in a full sequence of generalized St. Petersburg games, where a linear combination is viewed as the share of any
one of *n* cooperative gamblers who play with a pooling strategy. The expansions are given in terms of Fourier-Stieltjes transforms
and are constructed from suitably chosen members of the classes of subsequential semistable infinitely divisible asymptotic
distributions for the total winnings of the *n* players and from their pooling strategy, where the classes themselves are determined by the two parameters of the game. For
all values of the tail parameter, the expansions yield best possible rates of uniform merge. Surprisingly, it turns out that
for a subclass of strategies, not containing the averaging uniform strategy, our merging approximations reduce to asymptotic
expansions of the usual type, derived from a proper limiting distribution. The Fourier-Stieltjes transforms are shown to be
numerically invertible in general and it is also demonstrated that the merging expansions provide excellent approximations
even for very small *n*.

## Abstract

For the derivatives*p*
^{(k)}(x; α, γ) of the stable density of index α asymptotic formulae (of Plancherel Rotach type) are computed as*k*→∞ thereby exhibiting the detailed analytic structure for large orders of derivatives. Generalizing known results for the
special case of the one-sided stable laws (*O*<α<1, γ=-α) the whole range for the index of stability and the asymmetry parameter γ is covered.

## Abstract

The asymptotic behavior of the values of the integral of the Lebesgue function induced by interpolation at the Chebyshev roots is studied. Two leading terms in the corresponding asymptotic expansion are found explicitly.

A collector samples with replacement a set of
*n*
≧ 2 distinct coupons until he has
*n*
−
*m*
, 0 ≦
*m*
<
*n*
, distinct coupons for the first time. We refine the limit theorems concerning the standardized random number of necessary draws if
*n*
→ ∞ and
*m*
is fixed: we give a one-term asymptotic expansion of the distribution function in question, providing a better approximation of it, than the one given by the limiting distribution function, and proving in particular that the rate of convergence in these limiting theorems is of order (log
*n*
)/
*n*
.

## Summary

The asymptotic expansion of