F-homotopic transformations
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31: 20.10 Integrals
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§20.10(i) Mellin Transforms with respect to the Lattice Parameter
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20.10.1
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20.10.2
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20.10.3
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§20.10(ii) Laplace Transforms with respect to the Lattice Parameter
…32: 29.21 Tables
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Arscott and Khabaza (1962) tabulates the coefficients of the polynomials in Table 29.12.1 (normalized so that the numerically largest coefficient is unity, i.e. monic polynomials), and the corresponding eigenvalues for , . Equations from §29.6 can be used to transform to the normalization adopted in this chapter. Precision is 6S.
33: Bruce R. Miller
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►There, he carried out research in non-linear dynamics and celestial mechanics, developing a specialized computer algebra system for high-order Lie transformations.
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34: 9.10 Integrals
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§9.10(v) Laplace Transforms
… ►For Laplace transforms of products of Airy functions see Shawagfeh (1992). ►§9.10(vi) Mellin Transform
… ►§9.10(vii) Stieltjes Transforms
… ►§9.10(ix) Compendia
…35: 2.4 Contour Integrals
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►Then
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►For examples and extensions (including uniformity and loop integrals) see Olver (1997b, Chapter 4), Wong (1989, Chapter 1), and Temme (1985).
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§2.4(ii) Inverse Laplace Transforms
… ►Then the Laplace transform … ►For examples see Olver (1997b, pp. 315–320). …36: 19.22 Quadratic Transformations
§19.22 Quadratic Transformations
… ►Bartky’s Transformation
… ►Descending Gauss transformations include, as special cases, transformations of complete integrals into complete integrals; ascending Landen transformations do not. … ►37: 23.15 Definitions
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►Also denotes a bilinear transformation on , given by
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23.15.3
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►The set of all bilinear transformations of this form is denoted by SL (Serre (1973, p. 77)).
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23.15.5
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38: Guide to Searching the DLMF
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Table 1: Query Examples
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Query | Matching records contain |
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"Fourier transform" and series |
both the phrase “Fourier transform” and the word “series”. |
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Fourier (transform or series) |
at least one of “Fourier transform” or “Fourier series”. |
1/(2pi) and "Fourier transform" |
both and the phrase “Fourier transform”. |
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39: 16.16 Transformations of Variables
§16.16 Transformations of Variables
►§16.16(i) Reduction Formulas
… ►§16.16(ii) Other Transformations
… ►For quadratic transformations of Appell functions see Carlson (1976).40: Bille C. Carlson
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►The main theme of Carlson’s mathematical research has been to expose previously hidden permutation symmetries that can eliminate a set of transformations and thereby replace many formulas by a few.
…This symmetry led to the development of symmetric elliptic integrals, which are free from the transformations of modulus and amplitude that complicate the Legendre theory.
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