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Generalized q-Legendre Polynomials

Journal of Computational and Applied Mathematics, 1993
The author finds the polynomials \(u_ n\) satisfying the 3-term recursion: \[ (1-q^{n+1}) (1+q^ n) u_{n+1} - f_ nu_ n + q^{2n- 1} (1-q^ n) (1+q^{N+1}) u_{n-1} = 0, \] where \[ f_ n = (1- q^{2n+1}) \left( 2q^ n-(1+q^ n) (1+q^{n+1}) \sum_{j=0}^ nq^{-jn} \left[ {n \over j} \right]_ q \left[ {n+j \over j} \right]_ qx_ j \right). \] For \(x_ 0=x\), \(x_ j=0\
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On Legendre's Polynomials

1976
Publisher Summary This chapter focuses on Legendre's polynomials. It discusses Kodaira's identity, Weyl's theory, Green's formula, symmetric boundary conditions, T-positive theory, S-positive theory, and other theorems.
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Associated Legendre Polynomial Approximations

Journal of Applied Physics, 1951
Approximations for the associated Legendre Polynomials are derived by a phase integral method. The method is an extension of the WBK method, applicable to separable multidimensional wave propagation problems.
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Interval Analysis Method Based on Legendre Polynomial Approximation for Uncertain Multibody Systems

Advances in Engineering Software, 2018
Jinglai Wu, Xingxing Feng, Yunqing Zhang
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Adaptive Mesh Refinement Method for Optimal Control Using Decay Rates of Legendre Polynomial Coefficients

IEEE Transactions on Control Systems Technology, 2018
Anil Rao, William Ward Hager
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Legendre Polynomial

2021
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Legendre Polynomials

1998
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Legendre Polynomial Solutions of High-Order Linear Fredholm Integro-Differential Equations

Applied Mathematics and Computation, 2009
Hüseyin Hilmi Sorkun, Mehmet Sezer
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Legendre Polynomial

2020
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The Overlap Integral of Three Associated Legendre Polynomials

Applied Mathematics Letters, 2002
R Lemus
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