Legendre functions
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41—50 of 161 matching pages
41: 1 Algebraic and Analytic Methods
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42: 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
… ►43: 30.6 Functions of Complex Argument
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Relations to Associated Legendre Functions
…44: 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.
45: 16.18 Special Cases
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►As a corollary, special cases of the and
functions, including Airy functions, Bessel functions, parabolic cylinder functions, Ferrers functions, associated Legendre functions, and many orthogonal polynomials, are all special cases of the Meijer -function.
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46: 14.16 Zeros
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§14.16(iii) Interval
…47: 14.20 Conical (or Mehler) Functions
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►For and , a numerically satisfactory pair of real conical functions is and .
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14.20.6
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14.20.11
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14.20.12
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14.20.13
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48: Bibliography G
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Algorithm 259: Legendre functions for arguments larger than one.
Comm. ACM 8 (8), pp. 488–492.
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Integrals of three Bessel functions and Legendre functions. I.
J. Math. Phys. 26 (4), pp. 633–644.
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Integrals of three Bessel functions and Legendre functions. II.
J. Math. Phys. 26 (4), pp. 645–655.
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Evaluation of Legendre functions of argument greater than one.
Comput. Phys. Comm. 105 (2-3), pp. 273–283.
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