Geodesic
Complement of Jacobi matrix
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 2, pp. 161-170 
Yu. I. Kuznetsov. Complement of Jacobi matrix. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 2, pp. 161-170. http://geodesic.mathdoc.fr/item/SJVM_1999_2_2_a4/
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     title = {Complement of {Jacobi} matrix},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The new properties of Jacobi matrix are discussed. The matrix analogs for the differential operator of the hypergeometric type and of the Pearson one are derived on the base of Jacobi matrix properties exclusivly: the conjugate Sturm system is derived from the properties of symmetric Jacobi matrix $T$, as well as the complementary Jacobi matrix $T^c$, for which this conjugate Sturm system is an ordinary Sturm system.

[1] Kuznetsov Yu. I., “Svyaz polozhitelno-opredelennykh matrits i matrits Khessenberga”, Sib. mat. zhurn., 27:2 (1986), 94–100

[2] Ilin V. P., Kuznetsov Yu. I., Algebraicheskie osnovy chislennogo analiza, Nauka, Novosibirsk, 1986 | MR

[3] Nikiforov A. F., Uvarov V. B., Spetsialnye funktsii matematicheskoi fiziki, Nauka, M., 1978 | MR

[4] Suetin P. K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1976 | MR