# Search Results

## You are looking at 1 - 10 of 19 items for :

• "Asymptotic expansions"
• All content
Clear All

# Asymptotic expansion for log n! in terms of the reciprocal of a triangular number

Acta Mathematica Hungarica
Author: Gergő Nemes

] 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

Restricted access

# Asymptotic expansion and continued fraction for mathieu's series

Periodica Mathematica Hungarica
Author: Á. Elbert
Restricted access

# Asymptotic expansion of norm associated with conjugate trigonometric polynomial

Periodica Mathematica Hungarica
Author: T. Jiang

LetT n (x) be trigonometric polynomial of degreen, and be conjugation ofT n (x). In this paper we obtain the complete asymptotic expansion for

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$C_n = \mathop {\sup }\limits_{\left\| {T_n } \right\|C \leqslant 1} \left\| {\tilde T_n } \right\|_C$$ \end{document}
forn→∞.

Restricted access

# Polynomial asymptotic expansions in the real domain: the geometric, the factorizational, and the stabilization approaches

Analysis Mathematica
Author: Antonio Granata

## Abstract

The problem of the existence of an asymptotic expansion of type

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$f(x) = a_n x^n + a_{n - 1} x^{n - 1} + \cdots + a_i x^i + o(x^i ), x \to + \infty ,$$ \end{document}
is thoroughly studied, comparing and completing the known results obtained through the three different approaches mentioned in the title. A unifying thread is provided by the canonical factorizations of the differential operator D n. Particularly meaningful are several characterizations of the polynomial asymptotic expansions of an nth order convex function.

Restricted access

# Merging asymptotic expansions for cooperative gamblers in generalized St. Petersburg games

Acta Mathematica Hungarica
Authors: S. Csörgő and P. Kevei

## 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.

Restricted access

# Asymptotic expansions for derivatives of stable laws

Periodica Mathematica Hungarica
Author: M. Wiessner

## Abstract

For the derivativesp (k)(x; α, γ) of the stable density of index α asymptotic formulae (of Plancherel Rotach type) are computed ask→∞ 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.

Restricted access

# An asymptotic expansion for the weights of Gaussian quadrature formulae

Acta Mathematica Hungarica
Author: K. Petras
Restricted access

# On the Integral of the Lebesgue Function Induced by Interpolation at the Chebyshev Nodes

Acta Mathematica Hungarica
Authors: L. Brutman, I. Gopengauz, and D. Toledano

## 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.

Restricted access

# Asymptotic approximations for coupon collectors

Studia Scientiarum Mathematicarum Hungarica
Authors: Anna Pósfai and Sándor Csörgő

A collector samples with replacement a set of n ≧ 2 distinct coupons until he has nm , 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 .

Restricted access

# A remark on product partition

Acta Mathematica Hungarica
Authors: Imre Kátai and M. V. Subbarao

## Summary

The asymptotic expansion of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\sum\limits_{n\le x}e^*(n)$ \end{document} is given, where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $e^*(n)$ \end{document} is defined by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\sum{\frac{{e^*(n)}}{{n^s}}} = \prod\limits_{n=2}^\infty (1-1/n^s)$ \end{document}.

Restricted access