TY - JOUR
T1 - Jacobi-Sobolev-type orthogonal polynomials
T2 - holonomic equation and electrostatic interpretation - a non-diagonal case
AU - Dueñas, Herbert
AU - Garza, Luis E.
PY - 2013/1
Y1 - 2013/1
N2 - Consider the Sobolev-type inner product, where p and q are polynomials with real coefficients, α, β > -1, ℙ(x) = (p(x), p′(x))t, and, is a positive semidefinite matrix, with M0,M1≥0, and λ ∈ ℝ. We obtain an expression for the family of polynomials, orthogonal with respect to the above inner product, a connection formula that relates with some family of Jacobi polynomials and the holonomic equation that they satisfy, as well as an electrostatic interpretation of their zeros.
AB - Consider the Sobolev-type inner product, where p and q are polynomials with real coefficients, α, β > -1, ℙ(x) = (p(x), p′(x))t, and, is a positive semidefinite matrix, with M0,M1≥0, and λ ∈ ℝ. We obtain an expression for the family of polynomials, orthogonal with respect to the above inner product, a connection formula that relates with some family of Jacobi polynomials and the holonomic equation that they satisfy, as well as an electrostatic interpretation of their zeros.
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U2 - 10.1080/10652469.2012.668678
DO - 10.1080/10652469.2012.668678
M3 - Article
AN - SCOPUS:84872439880
SN - 1065-2469
VL - 24
SP - 70
EP - 83
JO - Integral Transforms and Special Functions
JF - Integral Transforms and Special Functions
IS - 1
ER -