scaling laws
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1: 36.6 Scaling Relations
§36.6 Scaling Relations
►Diffraction Catastrophe Scaling
… ►Indices for -Scaling of Magnitude of or (Singularity Index)
… ►Indices for -Scaling of Coordinates
… ►Indices for -Scaling of Hypervolume
…2: 27.9 Quadratic Characters
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27.9.2
►If are distinct odd primes, then the quadratic reciprocity law states that
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►Both (27.9.1) and (27.9.2) are valid with replaced by ; the reciprocity law (27.9.3) holds if are replaced by any two relatively prime odd integers .
3: 15.7 Continued Fractions
4: 15.15 Sums
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15.15.1
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5: 8.24 Physical Applications
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►The function appears in: discussions of power-law relaxation times in complex physical systems (Sornette (1998)); logarithmic oscillations in relaxation times for proteins (Metzler et al. (1999)); Gaussian orbitals and exponential (Slater) orbitals in quantum chemistry (Shavitt (1963), Shavitt and Karplus (1965)); population biology and ecological systems (Camacho et al. (2002)).
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6: Possible Errors in DLMF
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►One source of confusion, rather than actual errors, are some new functions which differ from those in Abramowitz and Stegun (1964) by scaling, shifts or constraints on the domain; see the Info box (click or hover over the icon) for links to defining formula.
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7: Bibliography F
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Application of the -function theory of Painlevé equations to random matrices: , the JUE, CyUE, cJUE and scaled limits.
Nagoya Math. J. 174, pp. 29–114.
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On the coefficients in the recursion formulae of orthogonal polynomials.
Proc. Roy. Irish Acad. Sect. A 76 (1), pp. 1–6.
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8: 15.6 Integral Representations
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►The function (not ) has the following integral representations:
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15.6.1
; .
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15.6.2
; , .
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15.6.8
; .
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15.6.9
; , .
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9: 33.22 Particle Scattering and Atomic and Molecular Spectra
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