eigenfunction expansions
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11—18 of 18 matching pages
11: 18.3 Definitions
12: Bibliography V
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On the series expansion method for computing incomplete elliptic integrals of the first and second kinds.
Math. Comp. 23 (105), pp. 61–69.
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Expansion of vacuum magnetic fields in toroidal harmonics.
Comput. Phys. Comm. 81 (1-2), pp. 74–90.
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Symbolic evaluation of coefficients in Airy-type asymptotic expansions.
J. Math. Anal. Appl. 269 (1), pp. 317–331.
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Expansions in products of Heine-Stieltjes polynomials.
Constr. Approx. 15 (4), pp. 467–480.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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13: 3.7 Ordinary Differential Equations
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►For classification of singularities of (3.7.1) and expansions of solutions in the neighborhoods of singularities, see §2.7.
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►The values are the eigenvalues and the corresponding solutions of the differential equation are the eigenfunctions.
The eigenvalues are simple, that is, there is only one corresponding eigenfunction (apart from a normalization factor), and when ordered increasingly the eigenvalues satisfy
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►The method consists of a set of rules each of which is equivalent to a truncated Taylor-series expansion, but the rules avoid the need for analytic differentiations of the differential equation.
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14: Bibliography R
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High precision Chebyshev expansions for Airy functions and their derivatives.
Technical report
University of Birmingham Computer Centre.
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On the computation of Lamé functions, of eigenvalues and eigenfunctions of some potential operators.
Z. Angew. Math. Mech. 78 (1), pp. 66–72.
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Partial fractions expansions and identities for products of Bessel functions.
J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
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15: 30.4 Functions of the First Kind
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►The eigenfunctions of (30.2.1) that correspond to the eigenvalues are denoted by , .
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§30.4(iii) Power-Series Expansion
… ►The expansion (30.4.7) converges in the norm of , that is, …It is also equiconvergent with its expansion in Ferrers functions (as in (30.4.2)), that is, the difference of corresponding partial sums converges to 0 uniformly for . …16: Bibliography K
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Hypergeometric expansions of Heun polynomials.
SIAM J. Math. Anal. 22 (5), pp. 1450–1459.
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Addendum: “Hypergeometric expansions of Heun polynomials”.
SIAM J. Math. Anal. 22 (6), pp. 1803.
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Series expansions for the third incomplete elliptic integral via partial fraction decompositions.
J. Comput. Appl. Math. 207 (2), pp. 331–337.
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Asymptotic expansions of certain -series and a formula of Ramanujan for specific values of the Riemann zeta function.
Acta Arith. 107 (3), pp. 269–298.
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Construction of differential operators having Bochner-Krall orthogonal polynomials as eigenfunctions.
J. Math. Anal. Appl. 324 (1), pp. 285–303.
17: Bibliography J
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Fonctions de Mathieu et fonctions propres de l’oscillateur relativiste.
Ann. Fac. Sci. Toulouse Math. (6) 7 (3), pp. 465–495 (French).
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A note on sampling expansion for a transform with parabolic cylinder kernel.
Inform. Sci. 26 (2), pp. 155–158.
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Uniform asymptotic expansions for Meixner polynomials.
Constr. Approx. 14 (1), pp. 113–150.
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Derivation of Green-type, transitional and uniform asymptotic expansions from differential equations. V. Angular oblate spheroidal wavefunctions and for large
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Proc. Roy. Soc. London Ser. A 321, pp. 545–555.
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18: 29.3 Definitions and Basic Properties
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►The eigenfunctions corresponding to the eigenvalues of §29.3(i) are denoted by , , , .
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Table 29.3.2: Lamé functions.
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