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1: 4.37 Inverse Hyperbolic Functions
§4.37 Inverse Hyperbolic Functions
… ►The principal values of the inverse hyperbolic cosecant, hyperbolic secant, and hyperbolic tangent are given by … ►Inverse Hyperbolic Sine
… ►Inverse Hyperbolic Cosine
… ►Inverse Hyperbolic Tangent
…2: 36.2 Catastrophes and Canonical Integrals
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Normal Forms for Umbilic Catastrophes with Codimension
… ►(hyperbolic umbilic). ►Canonical Integrals
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36.2.27
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36.2.29
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3: 4.35 Identities
§4.35 Identities
►§4.35(i) Addition Formulas
… ►§4.35(ii) Squares and Products
… ►§4.35(iii) Multiples of the Argument
… ►§4.35(iv) Real and Imaginary Parts; Moduli
…4: 20 Theta Functions
Chapter 20 Theta Functions
…5: 4.47 Approximations
§4.47 Approximations
►§4.47(i) Chebyshev-Series Expansions
►Clenshaw (1962) and Luke (1975, Chapter 3) give 20D coefficients for , , , , , , , , . … ►Hart et al. (1968) give , , , , , , , , , , , , , . … ►Luke (1975, Chapter 3) supplies real and complex approximations for , , , , , , . …6: 4.33 Maclaurin Series and Laurent Series
7: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Hill’s Equation.
Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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8: Bibliography G
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Contiguous relations and summation and transformation formulae for basic hypergeometric series.
J. Difference Equ. Appl. 19 (12), pp. 2029–2042.
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The solution of Cauchy’s problem for two totally hyperbolic linear differential equations by means of Riesz integrals.
Ann. of Math. (2) 48 (4), pp. 785–826.
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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