inversion
(0.001 seconds)
11—20 of 167 matching pages
11: 4.15 Graphics
…
►
§4.15(i) Real Arguments
… ►Figure 4.15.7 illustrates the conformal mapping of the strip onto the whole -plane cut along the real axis from to and to , where and (principal value). … ► ►§4.15(iii) Complex Arguments: Surfaces
… ►The corresponding surfaces for , , can be visualized from Figures 4.15.9, 4.15.11, 4.15.13 with the aid of equations (4.23.16)–(4.23.18).12: 19.10 Relations to Other Functions
…
►
►
►
►
…
►For relations to the Gudermannian function and its inverse
(§4.23(viii)), see (19.6.8) and
…
13: 4.46 Tables
§4.46 Tables
…14: 4.45 Methods of Computation
…
►
Inverse Trigonometric Functions
… ►Hyperbolic and Inverse Hyperbolic Functions
… ►The inverses , , and can be computed from the logarithmic forms given in §4.37(iv), with real arguments. For , , and we have (4.37.7)–(4.37.9). … ►Similarly for the hyperbolic and inverse hyperbolic functions; compare (4.28.1)–(4.28.7), §4.37(iv), and (4.37.7)–(4.37.9). …15: 4.39 Continued Fractions
§4.39 Continued Fractions
… ►
4.39.2
…
►
4.39.3
…
►For these and other continued fractions involving inverse hyperbolic functions see Lorentzen and Waadeland (1992, pp. 569–571).
…
16: 27.5 Inversion Formulas
§27.5 Inversion Formulas
… ►which, in turn, is the basis for the Möbius inversion formula relating sums over divisors: … ►Special cases of Möbius inversion pairs are: … ►Other types of Möbius inversion formulas include: … ►17: 4.40 Integrals
18: 27.17 Other Applications
§27.17 Other Applications
►Reed et al. (1990, pp. 458–470) describes a number-theoretic approach to Fourier analysis (called the arithmetic Fourier transform) that uses the Möbius inversion (27.5.7) to increase efficiency in computing coefficients of Fourier series. …19: Mark J. Ablowitz
…
►for appropriate data they can be linearized by the Inverse Scattering Transform (IST) and they possess solitons as special solutions.
…Some of the relationships between IST and Painlevé equations are discussed in two books: Solitons and the Inverse Scattering Transform and Solitons, Nonlinear Evolution Equations and Inverse Scattering.
…