A framework for conceptualizing the development of individual differences in reading ability is presented that synthesizes a great deal of the research literature. The framework places special emph...

Matthew effects in reading: Some consequences of individual differences in the acquisition of literacy.

Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

Analytic Combinatorics

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

We list the so-called Askey-scheme of hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation and generating functions of all classes of orthogonal polynomials in this scheme. In chapeter 2 we give all limit relation between different classes of orthogonal polynomials listed in the Askey-scheme. 
In chapter 3 we list the q-analogues of the polynomials in the Askey-scheme. We give their definition, orthogonality relation, three term recurrence relation and generating functions. In chapter 4 we give the limit relations between those basic hypergeometric orthogonal polynomials. Finally in chapter 5 we point out how the `classical` hypergeometric orthogonal polynomials of the Askey-scheme can be obtained from their q-analogues.

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The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

Global asymptotics of orthogonal polynomials associated with

Gerbils reared by rats: effects on adult open-field and ventral marking activity.

Asymptotics of orthogonal polynomials

A large number of important integral transforms, such as Laplace, Fourier sine and cosine, Hankel, Stieltjes, and Riemann- Liouville fractional integral transforms, can be put in the form 1.1 where f(t) and the kernel, h(t), are locally integrable functions on (0,∞), and x is a positive parameter. Recently, two important techniques have been developed to give asymptotic expansions of I(x) as x → + ∞ or x → 0+. One method relies heavily on the theory of Mellin transforms [8] and the other is based on the use of distributions [24]. Here, of course, the integral I(x) is assumed to exist in some ordinary sense. If the above integral does not exist in any ordinary sense, then it may be regarded as an integral transform of a distribution (generalized function). There are mainly two approaches to extend the classical integral transforms to distributions.

Generalized Mellin Convolutions and their Asymptotic Expansions

Explicit and realistic error bounds are constructed for a one-term and a two-term asymptotic approximation of the Jacobi function $\varphi _\mu ^{(\alpha ,\beta )} (t)$ as $\mu \to \infty $, uniformly for $t \in (0,\infty )$. A similar result is obtained for the zeros $t_{\mu ,k} $ of this function as $\mu \to \infty $, which holds uniformly with respect to unbounded k. Exponentially decaying error bounds are also given for asymptotic approximations of $\varphi _\mu ^{(\alpha ,\beta )} (t)$ as $t \to \infty $ and of $t_{\mu ,k} $ as $k \to \infty $, which are uniform for $\mu \geqq \delta > 0$.

Roderick Wong

Papers

Global asymptotics of orthogonal polynomials associated with

Gerbils reared by rats: effects on adult open-field and ventral marking activity.

Asymptotics of orthogonal polynomials

Generalized Mellin Convolutions and their Asymptotic Expansions

On the asymptotics of the Jacobi function and its zeros