Geodesic
Polynomials orthogonal with sign-sensitive weight
Matematičeskie zametki, Tome 59 (1996) no. 5, pp. 737-752

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We introduce the notion of inner product with sign-sensitive weight and construct systems of nonsymmetrically orthonormalized polynomials. We also study some properties of such polynomials (for example, the properties of Fourier coefficients, quadrature formulas of Gauss type, etc.). 
@article{MZM_1996_59_5_a9,
     author = {A. K. Ramazanov},
     title = {Polynomials orthogonal with sign-sensitive weight},
     journal = {Matemati\v{c}eskie zametki},
     pages = {737--752},
     publisher = {mathdoc},
     volume = {59},
     number = {5},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_5_a9/}
}
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A. K. Ramazanov. Polynomials orthogonal with sign-sensitive weight. Matematičeskie zametki, Tome 59 (1996) no. 5, pp. 737-752. http://geodesic.mathdoc.fr/item/MZM_1996_59_5_a9/