Van Vleck theorem
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1—10 of 150 matching pages
1: 1.12 Continued Fractions
2: 30.10 Series and Integrals
3: 19.35 Other Applications
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§19.35(i) Mathematical
►Generalizations of elliptic integrals appear in analysis of modular theorems of Ramanujan (Anderson et al. (2000)); analysis of Selberg integrals (Van Diejen and Spiridonov (2001)); use of Legendre’s relation (19.7.1) to compute to high precision (Borwein and Borwein (1987, p. 26)). …4: 31.15 Stieltjes Polynomials
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►The are called Van Vleck polynomials and the corresponding
Stieltjes polynomials.
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31.15.2
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►If is a zero of the Van Vleck polynomial , corresponding to an th degree Stieltjes polynomial , and are the zeros of (the derivative of ), then is either a zero of or a solution of the equation
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►See Marden (1966), Alam (1979), and Al-Rashed and Zaheer (1985) for further results on the location of the zeros of Stieltjes and Van Vleck polynomials.
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5: Bibliography
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Asymptotic expansions of spheroidal wave functions.
J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
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Zeros of Stieltjes and Van Vleck polynomials and applications.
J. Math. Anal. Appl. 110 (2), pp. 327–339.
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Zeros of Stieltjes and Van Vleck polynomials.
Trans. Amer. Math. Soc. 252, pp. 197–204.
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Theorems on generalized Dedekind sums.
Pacific J. Math. 2 (1), pp. 1–9.
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Continuous -Hermite Polynomials when
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In
-series and Partitions (Minneapolis, MN, 1988),
IMA Vol. Math. Appl., Vol. 18, pp. 151–158.
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6: 28.27 Addition Theorems
§28.27 Addition Theorems
►Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. They are analogous to the addition theorems for Bessel functions (§10.23(ii)) and modified Bessel functions (§10.44(ii)). …7: Bibliography V
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Calculation of spheroidal wave functions.
J. Acoust. Soc. Amer. 51, pp. 414–416.
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Accurate calculation of the modified Mathieu functions of integer order.
Quart. Appl. Math. 65 (1), pp. 1–23.
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Mathieu and Spheroidal Wave Functions: Fortran Programs for their Accurate Calculation
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Light Scattering by Small Particles.
John Wiley and Sons. Inc., New York.
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Multiple Light Scattering.
Vol. 1, Academic Press, New York.
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8: 25.6 Integer Arguments
9: 6.17 Physical Applications
10: Bibliography D
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Integralen voor de -functie van Riemann.
Mathematica (Zutphen) B5, pp. 170–180 (Dutch).
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Computing Riemann theta functions.
Math. Comp. 73 (247), pp. 1417–1442.
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Computing Riemann matrices of algebraic curves.
Phys. D 152/153, pp. 28–46.
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On Vandermonde’s theorem, and some more general expansions.
Proc. Edinburgh Math. Soc. 25, pp. 114–132.
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Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions.
Methods Appl. Anal. 6 (3), pp. 21–56.
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