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Multivariate Laguerre Polynomial

The multivariate Laguerre polynomials L_kappa^((alpha,gamma))(x_1,...,x_m) are symmetric polynomials orthogonal on [0,infty)^m with respect to the weight

W_L(x_1,...,x_m)=exp[-sum_(i=1)^mx_i]product_(i=1)^mx_i^gammaproduct_(1<=i<j<=m)|x_i-x_j|^(2/alpha),

where alpha>0 and gamma>-1 (Dumitriu et al. 2007). The family can be obtained as a limiting case of the multivariate Jacobi polynomials. When m=1, it reduces to the ordinary Laguerre polynomial family.

See also

Jack Polynomial, Laguerre Polynomial, Multivariate Hermite Polynomial, Multivariate Orthogonal Polynomials

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References

Dumitriu, I.; Edelman, A.; and Shuman, G. "MOPS: Multivariate Orthogonal Polynomials (Symbolically)." J. Symb. Comput. 42, 587-620, 2007. https://doi.org/10.1016/j.jsc.2007.01.005.

Cite this as:

Weisstein, Eric W. "Multivariate Laguerre Polynomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MultivariateLaguerrePolynomial.html

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