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11: 10.37 Inequalities; Monotonicity
See also Paltsev (1999), Petropoulou (2000), Segura (2011) and Gaunt (2014).
12: Mourad E. H. Ismail
Ismail was elected a fellow of the American Mathematical Society in 2014. …
13: Bibliography W
  • R. J. Wells (1999) Rapid approximation to the Voigt/Faddeeva function and its derivatives. J. Quant. Spect. and Rad. Transfer 62 (1), pp. 29–48.
  • J. A. Wilson (1980) Some hypergeometric orthogonal polynomials. SIAM J. Math. Anal. 11 (4), pp. 690–701.
  • G. Wolf (2008) On the asymptotic behavior of the Fourier coefficients of Mathieu functions. J. Res. Nat. Inst. Standards Tech. 113 (1), pp. 11–15.
  • R. Wong (2014) Asymptotics of linear recurrences. Anal. Appl. (Singap.) 12 (4), pp. 463–484.
  • E. M. Wright (1940b) The generalized Bessel function of order greater than one. Quart. J. Math., Oxford Ser. 11, pp. 36–48.
  • 14: Bibliography S
  • T. C. Scott, G. Fee, J. Grotendorst, and W. Z. Zhang (2014) Numerics of the generalized Lambert W function. ACM Commun. Comput. Algebra 48 (2), pp. 42–56.
  • R. Shail (1980) On integral representations for Lamé and other special functions. SIAM J. Math. Anal. 11 (4), pp. 702–723.
  • N. T. Shawagfeh (1992) The Laplace transforms of products of Airy functions. Dirāsāt Ser. B Pure Appl. Sci. 19 (2), pp. 7–11.
  • A. Sidi (2010) A simple approach to asymptotic expansions for Fourier integrals of singular functions. Appl. Math. Comput. 216 (11), pp. 3378–3385.
  • R. Sips (1965) Représentation asymptotique de la solution générale de l’équation de Mathieu-Hill. Acad. Roy. Belg. Bull. Cl. Sci. (5) 51 (11), pp. 1415–1446.
  • 15: Bibliography P
  • J. B. Parkinson (1969) Optical properties of layer antiferromagnets with K 2 NiF 4 structure. J. Phys. C: Solid State Physics 2 (11), pp. 2012–2021.
  • L. Piela (2014) Ideas of Quantum Chemistry. second edition, Elsevier, Amsterdam-New York.
  • R. Piessens and M. Branders (1984) Algorithm 28. Algorithm for the computation of Bessel function integrals. J. Comput. Appl. Math. 11 (1), pp. 119–137.
  • 16: 13.11 Series
    For other series expansions see Tricomi (1954, §1.8), Hansen (1975, §§66 and 87), Prudnikov et al. (1990, §6.6), López and Temme (2010a) and López and Pérez Sinusía (2014). …
    17: Bibliography N
  • E. Neuman (1969a) Elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 99–102.
  • E. Neuman (1969b) On the calculation of elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 91–94.
  • A. F. Nikiforov and V. B. Uvarov (1988) Special Functions of Mathematical Physics: A Unified Introduction with Applications. Birkhäuser Verlag, Basel.
  • 18: 4.13 Lambert W -Function
    d 0 = 1 , d 1 = 2 , d 2 = 2 3 , d 3 = 11 36 2 , d 4 = 43 135 ,
    For a generalization of the Lambert W -function connected to the three-body problem see Scott et al. (2006), Scott et al. (2013) and Scott et al. (2014).
    19: 2.9 Difference Equations
     Wang and Wong (2012) and Wong (2014). … Dai et al. (2014). …
    20: 10 Bessel Functions