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1: 22.8 Addition Theorems
Greenhill (1959, pp. 121–130) reviews these results in terms of the geometric poristic polygon constructions of Poncelet. …
2: 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. …
3: Bibliography H
  • P. Henrici (1986) Applied and Computational Complex Analysis. Vol. 3: Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons Inc.], New York.
  • N. J. Hitchin (1995) Poncelet Polygons and the Painlevé Equations. In Geometry and Analysis (Bombay, 1992), Ramanan (Ed.), pp. 151–185.
  • 4: Bibliography G
  • R. G. Gordon (1969) New method for constructing wavefunctions for bound states and scattering. J. Chem. Phys. 51, pp. 14–25.
  • R. G. Gordon (1970) Constructing wavefunctions for nonlocal potentials. J. Chem. Phys. 52, pp. 6211–6217.
  • A. J. Guttmann and T. Prellberg (1993) Staircase polygons, elliptic integrals, Heun functions, and lattice Green functions. Phys. Rev. E 47 (4), pp. R2233–R2236.
  • 5: 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. …
    6: 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. …
    7: 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. …
    8: Bruce R. Miller
    In particular, he developed the LaTeXML system used for converting the  source documents into XML and MathML from which the DLMF website is constructed. …
    9: 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. …
    10: 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 ). …