An extended Airy function of the first kind

Generating Functions for Extended Stirling Numbers of the First Kind

In this paper we extend the definition of Stirling numbers of the first kind by way of a special multiset. This results in a family of number triangles for which we show how to obtain ordinary generating functions for the rows and exponential generating functions for the columns. The latter are derived via a recursive process. We also indicate how to obtain formulas, in terms of factorials, gen...

An “Airy” Image

Solution of First kind Fredholm Integral Equation by Sinc Function

Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind ...

Numerical solution of the system of Volterra integral equations of the first kind

This paper presents a comparison between variational iteration method (VIM) and modfied variational iteration method (MVIM) for approximate solution a system of Volterra integral equation of the first kind. We convert a system of Volterra integral equations to a system of Volterra integro-di®erential equations that use VIM and MVIM to approximate solution of this system and hence obtain an appr...

Philippe Flajolet and the Airy Function

1. Historical backgrounds: the Airy function in Physics 2 2. The area-Airy distributions: Brownian motion, linear probing hashing, additive parameters in grammars 4 2.1. Area under a Brownian excursion 4 2.2. On the analysis of linear probing hashing 4 2.3. Analytic variations on the Airy distribution 5 2.4. Hachage, arbres, chemins & graphes 6 3. Random matrices, Airy kernel and the Tracy–Wido...