# construction

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## 1—10 of 63 matching pages

##### 1: 9.15 Mathematical Applications

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►Airy functions play an indispensable role in the construction of uniform asymptotic expansions for contour integrals with coalescing saddle points, and for solutions of linear second-order ordinary differential equations with a simple turning point.
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##### 2: 27.17 Other Applications

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►Congruences are used in constructing perpetual calendars, splicing telephone cables, scheduling round-robin tournaments, devising systematic methods for storing computer files, and generating pseudorandom numbers.
…Apostol and Zuckerman (1951) uses congruences to construct magic squares.
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##### 3: Joyce E. Conlon

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►In 1999 she joined the NIST Mathematical and Computational Sciences Division, where she contributed to the DLMF project, especially in the construction of the bibliography.
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##### 4: Tom H. Koornwinder

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►Currently he is on the editorial board for Constructive Approximation, and is editor for the volume on

*Multivariable Special Functions*in the ongoing Askey–Bateman book project. …##### 5: Bruce R. Miller

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►In particular, he developed the LaTeXML system used for converting the LaTeX source documents into XML and MathML from which the DLMF website is constructed.
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##### 6: Peter L. Walker

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►Walker’s books are

*An Introduction to Complex Analysis*, published by Hilger in 1974,*The Theory of Fourier Series and Integrals*, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and*Examples and Theorems in Analysis*, published by Springer in 2004. …##### 7: 10.72 Mathematical Applications

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►Bessel functions and modified Bessel functions are often used as approximants in the construction of uniform asymptotic approximations and expansions for solutions of linear second-order differential equations containing a parameter.
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►In regions in which (10.72.1) has a simple turning point ${z}_{0}$, that is, $f(z)$ and $g(z)$ are analytic (or with weaker conditions if $z=x$ is a real variable) and ${z}_{0}$ is a simple zero of $f(z)$, asymptotic expansions of the solutions $w$ for large $u$ can be constructed in terms of Airy functions or equivalently Bessel functions or modified Bessel functions of order $\frac{1}{3}$ (§9.6(i)).
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►If $f(z)$ has a double zero ${z}_{0}$, or more generally ${z}_{0}$ is a zero of order $m$, $m=2,3,4,\mathrm{\dots}$, then uniform asymptotic approximations (but

*not*expansions) can be constructed in terms of Bessel functions, or modified Bessel functions, of order $1/(m+2)$. … ►In regions in which the function $f(z)$ has a simple pole at $z={z}_{0}$ and ${(z-{z}_{0})}^{2}g(z)$ is analytic at $z={z}_{0}$ (the case $\lambda =-1$ in §10.72(i)), asymptotic expansions of the solutions $w$ of (10.72.1) for large $u$ can be constructed in terms of Bessel functions and modified Bessel functions of order $\pm \sqrt{1+4\rho}$, where $\rho $ is the limiting value of ${(z-{z}_{0})}^{2}g(z)$ as $z\to {z}_{0}$. … ►Then for large $u$ asymptotic approximations of the solutions $w$ can be constructed in terms of Bessel functions, or modified Bessel functions, of variable order (in fact the order depends on $u$ and $\alpha $). …##### 8: 13.27 Mathematical Applications

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►Vilenkin (1968, Chapter 8) constructs irreducible representations of this group, in which the diagonal matrices correspond to operators of multiplication by an exponential function.
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##### 9: Mourad E. H. Ismail

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►Ismail serves on several editorial boards including the Cambridge University Press book series

*Encyclopedia of Mathematics and its Applications*, and on the editorial boards of 9 journals including*Proceedings of the American Mathematical Society*(Integrable Systems and Special Functions Editor);*Constructive Approximation*;*Journal of Approximation Theory*; and*Integral Transforms and Special Functions*. …##### 10: Daniel W. Lozier

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►His research interests have centered on numerical analysis, special functions, computer arithmetic, and mathematical software construction and testing.
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