associated Legendre functions
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31—40 of 66 matching pages
31: 14.33 Tables
§14.33 Tables
…32: 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
… ►33: Bibliography S
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Evaluation of associated Legendre functions off the cut and parabolic cylinder functions.
Electron. Trans. Numer. Anal. 9, pp. 137–146.
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The expansion of Lamé functions into series of associated Legendre functions of the second kind.
Proc. Cambridge Philos. Soc. 62, pp. 441–452.
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On the derivative of the associated Legendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order).
J. Math. Chem. 46 (1), pp. 231–260.
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On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order).
J. Math. Chem. 49 (7), pp. 1436–1477.
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On parameter derivatives of the associated Legendre function of the first kind (with applications to the construction of the associated Legendre function of the second kind of integer degree and order).
J. Math. Anal. Appl. 386 (1), pp. 332–342.
34: 14.16 Zeros
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§14.16(iii) Interval
…35: 14.11 Derivatives with Respect to Degree or Order
§14.11 Derivatives with Respect to Degree or Order
…36: 10.54 Integral Representations
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►For the Legendre polynomial and the associated Legendre function
see §§18.3 and 14.21(i), with and .
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37: Mathematical Introduction
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►Other examples are: (a) the notation for the Ferrers functions—also known as associated Legendre functions on the cut—for which existing notations can easily be confused with those for other associated Legendre functions (§14.1); (b) the spherical Bessel functions for which existing notations are unsymmetric and inelegant (§§10.47(i) and 10.47(ii)); and (c) elliptic integrals for which both Legendre’s forms and the more recent symmetric forms are treated fully (Chapter 19).
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38: Bibliography V
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Generalized Associated Legendre Functions and their Applications.
World Scientific Publishing Co. Inc., Singapore.
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39: 10.19 Asymptotic Expansions for Large Order
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10.19.9
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40: Bibliography D
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Uniform asymptotic expansions for associated Legendre functions of large order.
Proc. Roy. Soc. Edinburgh Sect. A 133 (4), pp. 807–827.
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Convergent expansions for solutions of linear ordinary differential equations having a simple pole, with an application to associated Legendre functions.
Stud. Appl. Math. 113 (3), pp. 245–270.
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