Results 101 to 110 of about 292,163 (222)

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\
openaire   +2 more sources

Conférence de M. Pierre Legendre

, 1997
Legendre Pierre. Conférence de M. Pierre Legendre. In: École pratique des hautes études, Section des sciences religieuses. Annuaire. Tome 106, 1997-1998. 1997. pp.
Legendre, Pierre
core  

Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations

International Journal of Mathematics and Mathematical Sciences, 2011
We extend a collocation method for solving a nonlinear ordinary differential equation (ODE) via Jacobi polynomials. To date, researchers usually use Chebyshev or Legendre collocation method for solving problems in
Ahmad Imani, Azim Aminataei, Ali Imani
doaj   +1 more source

On the computation of discrete Legendre polynomial coefficients

, 1992
A new and fast method to find the discrete Legendre polynomial (DLP) coefficients is presented. The method is based on forming a simple matrix using addition only and then multiplying two elements of the matrix to compute the DLP ...
Aburdene, Maurice F., Dorband, J. E.
core   +1 more source

Interpretable coal mine fault detection via orthogonal Kolmogorov–Arnold networks

Scientific Reports
The continuous monitoring of safety within underground coal mines generates multivariate sensor data of high dimensionality, posing substantial challenges for accurate and interpretable fault detection in safety-critical industrial environments. Existing
Xueliang Jin, Zhihai Jiang, Qianyao Wang, Rui Shan   +3 more
doaj   +1 more source

Time-Domain Dynamics of Fractional Viscoelastic Spinning Disks via Shifted Legendre Polynomials

Fractal and Fractional
This paper presents a novel algorithm for the dynamic analysis of fractional-order viscoelastic spinning disks in the time domain. The novelty mainly lies in the use of the shifted Legendre polynomial algorithm for the direct time-domain numerical ...
Yuxuan Ma, Chunxiao Yu, Yiming Chen, Gang Cheng, Yongxing Wang   +4 more
doaj   +1 more source

Conférence de M. Pierre Legendre

, 1989
Legendre Pierre. Conférence de M. Pierre Legendre. In: École pratique des hautes études, Section des sciences religieuses. Annuaire. Tome 98, 1989-1990. 1989. pp.
Legendre, Pierre
core  

Conférence de M. Pierre Legendre

, 1978
Legendre Pierre. Conférence de M. Pierre Legendre. In: École pratique des hautes études, Section des sciences religieuses. Annuaire. Tome 88, 1979-1980. 1979.
Legendre, Pierre
core  

Conférence de M. Pierre Legendre

, 1996
Legendre Pierre. Conférence de M. Pierre Legendre. In: École pratique des hautes études, Section des sciences religieuses. Annuaire. Tome 105, 1996-1997. 1996. pp.
Legendre, Pierre
core  

Hierarchical intonation modelling for speech synthesis using Legendre polynomial coefficients [PDF]

Synthetic speech quality is now close to parity with human speech for isolated read speech utterances. There has therefore been a resurgence of interest in using speech synthesis for speech science research.
Corkey, Niamh, Lai, Catherine, Klabbers, Esther, O'Mahony, Johannah, King, Simon; id_orcid   +4 more
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