Orthogonal Polynomials With Weight Function (1 - x)α ( l + x)β + M δ(x + 1) + Nδ(x - 1)
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 205-214
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We study orthogonal polynomials for which the weight function is a linear combination of the Jacobi weight function and two delta functions at 1 and — 1. These polynomials can be expressed as 4 F 3 hypergeometric functions and they satisfy second order differential equations. They include Krall’s Jacobi type polynomials as special cases. The fourth order differential equation for the latter polynomials is derived in a more simple way.
Koornwinder, Tom H. Orthogonal Polynomials With Weight Function (1 - x)α ( l + x)β + M δ(x + 1) + Nδ(x - 1). Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 205-214. doi: 10.4153/CMB-1984-030-7
@article{10_4153_CMB_1984_030_7,
author = {Koornwinder, Tom H.},
title = {Orthogonal {Polynomials} {With} {Weight} {Function} (1 - x)\ensuremath{\alpha} ( l + x)\ensuremath{\beta} + {M} \ensuremath{\delta}(x + 1) + {N\ensuremath{\delta}(x} - 1)},
journal = {Canadian mathematical bulletin},
pages = {205--214},
year = {1984},
volume = {27},
number = {2},
doi = {10.4153/CMB-1984-030-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-030-7/}
}
TY - JOUR AU - Koornwinder, Tom H. TI - Orthogonal Polynomials With Weight Function (1 - x)α ( l + x)β + M δ(x + 1) + Nδ(x - 1) JO - Canadian mathematical bulletin PY - 1984 SP - 205 EP - 214 VL - 27 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-030-7/ DO - 10.4153/CMB-1984-030-7 ID - 10_4153_CMB_1984_030_7 ER -
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