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1: 10.73 Physical Applications
See Krivoshlykov (1994, Chapter 2, §2.2.10; Chapter 5, §5.2.2), Kapany and Burke (1972, Chapters 4–6; Chapter 7, §A.1), and Slater (1942, Chapter 4, §§20, 25). … More recently, Bessel functions appear in the inverse problem in wave propagation, with applications in medicine, astronomy, and acoustic imaging. …
§10.73(iii) Kelvin Functions
§10.73(iv) Bickley Functions
2: Bibliography K
  • R. B. Kearfott, M. Dawande, K. Du, and C. Hu (1994) Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.
  • M. K. Kerimov (1980) Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
  • A. V. Kitaev and A. H. Vartanian (2004) Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.
  • T. H. Koornwinder (2009) The Askey scheme as a four-manifold with corners. Ramanujan J. 20 (3), pp. 409–439.
  • V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin (1993) Quantum Inverse Scattering Method and Correlation Functions. Cambridge University Press, Cambridge.
  • 3: 12.10 Uniform Asymptotic Expansions for Large Parameter
    The turning points can be included if expansions in terms of Airy functions are used instead of elementary functions2.8(iii)). …
    §12.10(vi) Modifications of Expansions in Elementary Functions
    Inversely, with w = 2 1 3 ζ , …
    Modified Expansions
    4: Errata
  • Subsection 19.11(i)

    A sentence and unnumbered equation

    R C ( γ δ , γ ) = 1 δ arctan ( δ sin θ sin ϕ sin ψ α 2 1 α 2 cos θ cos ϕ cos ψ ) ,

    were added which indicate that care must be taken with the multivalued functions in (19.11.5). See (Cayley, 1961, pp. 103-106).

    Suggested by Albert Groenenboom.

  • Figure 4.3.1

    This figure was rescaled, with symmetry lines added, to make evident the symmetry due to the inverse relationship between the two functions.

    See accompanying text

    Reported 2015-11-12 by James W. Pitman.

  • Equations (4.23.34) and (4.23.35)
    4.23.34 arcsin z = arcsin β + i sign ( y ) ln ( α + ( α 2 1 ) 1 / 2 )

    and

    4.23.35 arccos z = arccos β i sign ( y ) ln ( α + ( α 2 1 ) 1 / 2 )

    Originally the factor sign ( y ) was missing from the second term on the right sides of these equations. Additionally, the condition for the validity of these equations has been weakened.

    Reported 2013-07-01 by Volker Thürey.

  • Equations (4.45.8), (4.45.9)

    These equations have been rewritten to improve the numerical computation of arctan x .

  • Chapters 8, 20, 36

    Several new equations have been added. See (8.17.24), (20.7.34), §20.11(v), (26.12.27), (36.2.28), and (36.2.29).