homogeneous%20harmonic%20polynomials
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1: 14.30 Spherical and Spheroidal Harmonics
§14.30 Spherical and Spheroidal Harmonics
… βΊ … βΊIn general, spherical harmonics are defined as the class of homogeneous harmonic polynomials. See Andrews et al. (1999, Chapter 9). … βΊ2: 31.5 Solutions Analytic at Three Singularities: Heun Polynomials
§31.5 Solutions Analytic at Three Singularities: Heun Polynomials
… βΊ
31.5.2
βΊis a polynomial of degree , and hence a solution of (31.2.1) that is analytic at all three finite singularities .
These solutions are the Heun polynomials.
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3: 35.4 Partitions and Zonal Polynomials
§35.4 Partitions and Zonal Polynomials
… βΊNormalization
… βΊOrthogonal Invariance
… βΊSummation
… βΊMean-Value
…4: 24.1 Special Notation
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Bernoulli Numbers and Polynomials
βΊThe origin of the notation , , is not clear. … βΊEuler Numbers and Polynomials
… βΊThe notations , , as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …5: 18.3 Definitions
§18.3 Definitions
… βΊFor expressions of ultraspherical, Chebyshev, and Legendre polynomials in terms of Jacobi polynomials, see §18.7(i). …For explicit power series coefficients up to for these polynomials and for coefficients up to for Jacobi and ultraspherical polynomials see Abramowitz and Stegun (1964, pp. 793–801). … βΊBessel polynomials
βΊBessel polynomials are often included among the classical OP’s. …6: Bibliography G
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Computing the zeros and turning points of solutions of second order homogeneous linear ODEs.
SIAM J. Numer. Anal. 41 (3), pp. 827–855.
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Analysis in homogeneous domains.
Uspehi Mat. Nauk 19 (4 (118)), pp. 3–92 (Russian).
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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7: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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Über lineare homogene Differentialgleichungen zweiter Ordnung mit drei im Endlichen gelegenen wesentlich singulären Stellen.
Math. Ann. 63 (3), pp. 301–321.
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8: 20 Theta Functions
Chapter 20 Theta Functions
…9: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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On the choice of standard solutions for a homogeneous linear differential equation of the second order.
Quart. J. Mech. Appl. Math. 3 (2), pp. 225–235.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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