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11: Wadim Zudilin
He has been an Associate Professor at Moscow State University (Russia), an Ostrowski Fellow at Institut Henri Poincaré and Université Paris 6 (France), a Humboldt Fellow at the Cologne University (Germany) and a Visiting Researcher at the Max Planck Institute for Mathematics in Bonn (Germany). …
12: 5.20 Physical Applications
Suppose the potential energy of a gas of n point charges with positions x 1 , x 2 , , x n and free to move on the infinite line < x < , is given by … For n charges free to move on a circular wire of radius 1 , …
13: Bibliography
  • G. Allasia and R. Besenghi (1987a) Numerical computation of Tricomi’s psi function by the trapezoidal rule. Computing 39 (3), pp. 271–279.
  • G. Allasia and R. Besenghi (1991) Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule. Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.
  • G. Allasia and R. Besenghi (1987b) Numerical calculation of incomplete gamma functions by the trapezoidal rule. Numer. Math. 50 (4), pp. 419–428.
  • G. Allasia and R. Besenghi (1989) Numerical Calculation of the Riemann Zeta Function and Generalizations by Means of the Trapezoidal Rule. In Numerical and Applied Mathematics, Part II (Paris, 1988), C. Brezinski (Ed.), IMACS Ann. Comput. Appl. Math., Vol. 1, pp. 467–472.
  • Axiom (free interactive system) Center for Algorithms and Interactive Scientific Software.
  • 14: 16.10 Expansions in Series of F q p Functions
    Here α , β , and γ are free real or complex parameters. …
    15: 21.9 Integrable Equations
    These parameters, including 𝛀 , are not free: they are determined by a compact, connected Riemann surface (Krichever (1976)), or alternatively by an appropriate initial condition u ( x , y , 0 ) (Deconinck and Segur (1998)). …
    16: 18.21 Hahn Class: Interrelations
    See accompanying text
    Figure 18.21.1: Askey scheme. The number of free real parameters is zero for Hermite polynomials. It increases by one for each row ascended in the scheme, culminating with four free real parameters for the Wilson and Racah polynomials. … Magnify
    17: Bibliography E
  • F. H. L. Essler, H. Frahm, A. R. Its, and V. E. Korepin (1996) Painlevé transcendent describes quantum correlation function of the X X Z antiferromagnet away from the free-fermion point. J. Phys. A 29 (17), pp. 5619–5626.
  • 18: Bibliography C
  • CAOP (website) Work Group of Computational Mathematics, University of Kassel, Germany.
  • CEPHES (free C library)
  • CoStLy (free C-XSC library)
  • 19: Bibliography L
  • D. Le (1985) An efficient derivative-free method for solving nonlinear equations. ACM Trans. Math. Software 11 (3), pp. 250–262.
  • D. W. Lozier and F. W. J. Olver (1994) Numerical Evaluation of Special Functions. In Mathematics of Computation 1943–1993: A Half-Century of Computational Mathematics (Vancouver, BC, 1993), Proc. Sympos. Appl. Math., Vol. 48, pp. 79–125.
  • 20: 28.33 Physical Applications
    We shall derive solutions to the uniform, homogeneous, loss-free, and stretched elliptical ring membrane with mass ρ per unit area, and radial tension τ per unit arc length. …