inverse%20trigonometric%20functions
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1: 10.73 Physical Applications
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►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).
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►More recently, Bessel functions appear in the inverse problem in wave propagation, with applications in medicine, astronomy, and acoustic imaging.
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§10.73(iii) Kelvin Functions
… ►§10.73(iv) Bickley Functions
…2: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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Quantum Inverse Scattering Method and Correlation Functions.
Cambridge University Press, Cambridge.
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3: 12.10 Uniform Asymptotic Expansions for Large Parameter
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►The turning points can be included if expansions in terms of Airy functions are used instead of elementary functions (§2.8(iii)).
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§12.10(vi) Modifications of Expansions in Elementary Functions
… ►Inversely, with , … ►Modified Expansions
… ►4: Errata
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Subsection 19.11(i)
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Figure 4.3.1
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Equations (4.23.34) and (4.23.35)
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Equations (4.45.8), (4.45.9)
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Chapters 8, 20, 36
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A sentence and unnumbered equation
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.
This figure was rescaled, with symmetry lines added, to make evident the symmetry due to the inverse relationship between the two functions.
Reported 2015-11-12 by James W. Pitman.
4.23.34
and
4.23.35
Originally the factor 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.
These equations have been rewritten to improve the numerical computation of .