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1: 9.15 Mathematical Applications
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. …
2: 27.17 Other Applications
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. …
3: Joyce E. Conlon
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. …
4: Tom H. Koornwinder
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
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. …
6: Peter L. Walker
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
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. … 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 1 3 9.6(i)). … If f ( z ) has a double zero z 0 , or more generally z 0 is a zero of order m , m = 2 , 3 , 4 , , 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 λ = - 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 ± 1 + 4 ρ , where ρ is the limiting value of ( z - z 0 ) 2 g ( z ) as z 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 α ). …
8: 13.27 Mathematical Applications
Vilenkin (1968, Chapter 8) constructs irreducible representations of this group, in which the diagonal matrices correspond to operators of multiplication by an exponential function. …
9: Mourad E. H. Ismail
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
His research interests have centered on numerical analysis, special functions, computer arithmetic, and mathematical software construction and testing. …