associated Legendre equation
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21—30 of 37 matching pages
21: Bibliography C
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The second Painlevé equation, its hierarchy and associated special polynomials.
Nonlinearity 16 (3), pp. R1–R26.
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The third Painlevé equation and associated special polynomials.
J. Phys. A 36 (36), pp. 9507–9532.
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The fourth Painlevé equation and associated special polynomials.
J. Math. Phys. 44 (11), pp. 5350–5374.
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Multi-Integral Representations for Associated Legendre and Ferrers Functions.
Symmetry 12 (10).
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On parameter differentiation for integral representations of associated Legendre functions.
SIGMA Symmetry Integrability Geom. Methods Appl. 7, pp. Paper 050, 16.
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22: 14.32 Methods of Computation
23: Bibliography O
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Studies on the Painlevé equations. I. Sixth Painlevé equation
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Ann. Mat. Pura Appl. (4) 146, pp. 337–381.
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Studies on the Painlevé equations. II. Fifth Painlevé equation
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Japan. J. Math. (N.S.) 13 (1), pp. 47–76.
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Associated Legendre functions on the cut.
J. Comput. Phys. 51 (3), pp. 502–518.
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Bessel Functions. Part III: Zeros and Associated Values.
Royal Society Mathematical Tables, Volume 7, Cambridge University Press, Cambridge-New York.
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Legendre functions with both parameters large.
Philos. Trans. Roy. Soc. London Ser. A 278, pp. 175–185.
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24: 14.5 Special Values
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14.5.14
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25: 14.18 Sums
26: Bibliography B
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On the Associated Legendre Polynomials.
In Orthogonal Expansions and their Continuous Analogues (Proc.
Conf., Edwardsville, Ill., 1967),
pp. 43–50.
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Tables of Normalized Associated Legendre Polynomials.
Pergamon Press, The Macmillan Co., Oxford-New York.
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Orthogonality relations for the associated Legendre functions of imaginary order.
Integral Transforms Spec. Funct. 24 (4), pp. 331–337.
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Asymptotic Expansions for the Coefficient Functions Associated with Linear Second-order Differential Equations: The Simple Pole Case.
In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.),
Lecture Notes in Pure and Applied Mathematics, Vol. 124, pp. 53–73.
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Associated Legendre polynomials, ordinary and modified spherical harmonics.
Comput. Phys. Comm. 5 (5), pp. 390–394.
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27: 30.6 Functions of Complex Argument
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►For results for Equation (30.2.1) with complex parameters see Meixner and Schäfke (1954).
Relations to Associated Legendre Functions
►28: Bibliography V
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Integrating products of Bessel functions with an additional exponential or rational factor.
Comput. Phys. Comm. 178 (8), pp. 578–590.
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A Mathieu equation for ships rolling among waves. I, II.
Norske Vid. Selsk. Forh., Trondheim 22 (25–26), pp. 113–123.
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Generalized Associated Legendre Functions and their Applications.
World Scientific Publishing Co. Inc., Singapore.
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On the growth of convergence radii for the eigenvalues of the Mathieu equation.
Math. Nachr. 192, pp. 239–253.
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On the rational solutions of the second Painlevé equation.
Differ. Uravn. 1 (1), pp. 79–81 (Russian).
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29: 14.15 Uniform Asymptotic Approximations
§14.15 Uniform Asymptotic Approximations
►§14.15(i) Large , Fixed
… ►For asymptotic expansions and explicit error bounds, see Dunster (2003b). ►§14.15(iii) Large , Fixed
… ►30: Bille C. Carlson
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► 2013) was Professor Emeritus in the Department of Mathematics and Associate of the Ames Laboratory (U.
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►This symmetry led to the development of symmetric elliptic integrals, which are free from the transformations of modulus and amplitude that complicate the Legendre theory.
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►This invariance usually replaces sets of twelve equations by sets of three equations and applies also to the relation between the first symmetric elliptic integral and the Jacobian functions.
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