Realizing the Calculation of a Fully Normalized Associated Legendre Function Based on an FPGA [PDF]
SensorsA large number of fully normalized associated Legendre function (fnALF) calculations are required to compute Earth’s gravity field elements using ultra high-order gravity field coefficient models.
Yuxiang Fang, Qingbin Wang, Yichao Yang
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Stability of Traveling Waves Based upon the Evans Function and Legendre Polynomials [PDF]
Applied Sciences, 2020 One of the tools and techniques concerned with the stability of nonlinear waves is the Evans function which is an analytic function whose zeros give the eigenvalues of the linearized operator.
H. M. Srivastava +2 more
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A note on dual integral equations involving associated Legendre function [PDF]
International Journal of Mathematics and Mathematical Sciences, 1992 This note is concerned with a formal method to obtain a closed form solution of certain dual integral equations involving the associated Legendre function P−1/2+iτμ(coshα) as kernel.
B. N. Mandal
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Multi-Integral Representations for Associated Legendre and Ferrers Functions [PDF]
Symmetry, 2020 For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions generalize some classical multi-integration formulas. As a result of the determination of these formulae, we compute some
Howard S. Cohl, Roberto S. Costas-Santos
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Integral of Legendre polynomials and its properties [PDF]
Mathematics and Computational SciencesThis paper is concerned with deriving a new system of orthogonal polynomials whose inflection points coincide with their interior roots, primitives of Legendre polynomials.
Abdelhamid Rehouma
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On Parameter Differentiation for Integral Representations of Associated Legendre Functions [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters.
Howard S. Cohl
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Expansion of a class of functions into an integral involving associated Legendre functions [PDF]
International Journal of Mathematics and Mathematical Sciences, 1994 A theorem for expansion of a class of functions into an integral involving associated Legendre functions is obtained in this paper.
Nanigopal Mandal, B. N. Mandal
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Fast computation of sine/cosine series coefficients of associated Legendre function of arbitrary high degree and order [PDF]
Journal of Geodetic Science, 2018 In order to accelerate the spherical/spheroidal harmonic synthesis of any function, we developed a new recursive method to compute the sine/cosine series coefficient of the 4π fully- and Schmidt quasi-normalized associated Legendre functions.
Fukushima T.
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Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments [PDF]
Advances in High Energy Physics, 2017 We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. Its generating function is applied to obtain an analytical result for a class of interesting integrals involving ...
Wei Li, Chang-Yuan Chen, Shi-Hai Dong
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The generalized associated Legendre functions [PDF]
, 2001 Mathematics Subject Classification: 33C60, 33C20, 44A15This paper is devoted to an important case of Wright’s hypergeometric function 2Fτ,β1(a, b; c; z) = 2Fτ,β1(z), to studying its basic properties and to application of 2Fτ,β1(z) to the generalization ...
Virchenko, Nina, Rumiantseva, Olena
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