Geodesic
The orthogonal and the nodal polynomials
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 2, pp. 137-145.

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The polynomials $P_k(x)$ of the degree $k$ that are orthogonal on a finite set of the points $x_i$, $i=1(1)n$, with weights $c_i>0$, are considered. It is shown that the polynomial $P_k(x)$ is a linear functional of the nodal polynomials of the same degree, expressed by $x_i$, $c_i$. The vector that defines this functional is positive and normalized. Such properties of the functional describe it as average, or the center of mass, of the nodal polynomials distributed with the corresponding density. 
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Yu. I. Kuznetsov. The orthogonal and the nodal polynomials. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 2, pp. 137-145. http://geodesic.mathdoc.fr/item/SJVM_2006_9_2_a2/

[1] Kuznetsov Yu. I., “Dopolnenie yakobievoi matritsy”, Sib. zhurn. vychisl. matematiki / RAN. Sib. otd-nie. — Novosibirsk, 2:2 (1999), 161–170 | Zbl

[2] Kuznetsov Yu. I., “Psevdoortogonalnye mnogochleny”, Sib. mat. zhurn., 42:6 (2001), 1314–1323 | MR | Zbl

[3] Kuznetsov Yu. I., “Gamiltonova forma yakobievoi matritsy”, Sib. zhurn. vychisl. matematiki / RAN. Sib. otd-nie, 3:2 (2000), 159–164 | MR | Zbl

[4] Kuznetsov Yu. I., “Tsiklicheskie matritsy i mnogochleny Chebysheva”, Sib. zhurn. vychisl. matematiki / RAN. Sib. otd-nie. — Novosibirsk, 4:4 (2001), 361–371 | Zbl

[5] Donoghue W. F., Matrix function and analitic continuation, Springer, New York, 1974 | MR | Zbl

[6] Nikiforov A. F., Suslov S. K., Uvarov V. B., Klassicheskie ortogonalnye polinomy diskretnoi peremennoi, Nauka, M., 1985 | MR

[7] Kuznetsov Yu. I., Elementy analiza na konechnom mnozhestve tochek, Izd-vo VTs SO RAN, Novosibirsk, 1994 | MR

[8] Kuznetsov Yu. I., Matritsy i mnogochleny, ch. 2, Izd-vo IVMiMG, Novosibirsk, 2004