Geodesic
Classical orthogonal polynomials of A discrete variable and representations of the three-dimensional rotation group
Funkcionalʹnyj analiz i ego priloženiâ, Tome 19 (1985) no. 3, pp. 22-35.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{FAA_1985_19_3_a2,
     author = {A. F. Nikiforov and S. K. Suslov and V. B. Uvarov},
     title = {Classical orthogonal polynomials of {A} discrete variable and representations of the three-dimensional rotation group},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {22--35},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_1985_19_3_a2/}
}
TY  - JOUR
AU  - A. F. Nikiforov
AU  - S. K. Suslov
AU  - V. B. Uvarov
TI  - Classical orthogonal polynomials of A discrete variable and representations of the three-dimensional rotation group
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 1985
SP  - 22
EP  - 35
VL  - 19
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_1985_19_3_a2/
LA  - ru
ID  - FAA_1985_19_3_a2
ER  - 
%0 Journal Article
%A A. F. Nikiforov
%A S. K. Suslov
%A V. B. Uvarov
%T Classical orthogonal polynomials of A discrete variable and representations of the three-dimensional rotation group
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 1985
%P 22-35
%V 19
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_1985_19_3_a2/
%G ru
%F FAA_1985_19_3_a2
A. F. Nikiforov; S. K. Suslov; V. B. Uvarov. Classical orthogonal polynomials of A discrete variable and representations of the three-dimensional rotation group. Funkcionalʹnyj analiz i ego priloženiâ, Tome 19 (1985) no. 3, pp. 22-35. http://geodesic.mathdoc.fr/item/FAA_1985_19_3_a2/

[1] Nikiforov A.F., Suslov S.K., Uvarov V.B., Postroenie chastnykh reshenii dlya raznostnogo uravneniya gipergeometricheskogo tipa, Preprint IPM im. M.V. Keldysha AN SSSR No142, 1984 | MR

[2] Nikiforov A., Ouvarov F., Fonctions Speciales de la Physique Mathematique, Editions Mir, Moscou, 1983

[3] Chebyshev P.L., Polnoe sobranie sochinenii, tt. 2, 3, Izd. AN SSSR, M., 1947, 1948 ; т. 2; т. 3 | MR

[4] Hahn W., “Über orthogonal Polynome, die $q$-Differenzengleichungen Genügen”, Math. Nachr., 2 (1949), 4–34 | DOI | MR | Zbl

[5] Weber M., Erdelyi A., “On the finite difference analogue of Rodrigues formula”, Amer. Math. Monthly, 59 (1952), 163–168 | DOI | MR | Zbl

[6] Karlin S., McGregor J.L., “The Hahn polynomials, formulas and application”, Scripta Math., 26 (1961), 33–46 | MR | Zbl

[7] Segë G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[8] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, t. 2, Nauka, M., 1973

[9] Nikiforov A.F., Uvarov A.F., Spetsialnye funktsii matematicheskoi fiziki, Nauka, M., 1984 | MR

[10] Askey R., Wilson J.A., “A set of orthogonal polynomials that generalize the Racah coefficients or $6j$-symbols”, SIAM J. Math. Anal., 10 (1979), 1008–1016 | DOI | MR | Zbl

[11] Wilson J.A., “Some hypergeometric orthogonal polynomials”, SIAM J. Math. Anal., 11 (1980), 690–701 | DOI | MR | Zbl

[12] Nikiforov A.F., Suslov S.K., Uvarov V.B., Polinomy Raka i dualnye polinomy Khana kak obobschenie klassicheskikh ortogonalnykh polinomov diskretnoi peremennoi, Preprint IPM im. M.V. Keldysha No 165, 1982 | MR

[13] Askey R., Wilson J., “A Set of Hypergeometric Orthogonal Polynomials”, SIAM J. Math. Anal., 13 (1982), 651–655 | DOI | MR | Zbl

[14] Nikiforov A.F., Uvarov V.B., Klassicheskie ortogonalnye polinomy diskretnoi peremennoi na neravnomernykh setkakh, Preprint IPM im. M.V. Keldysha AN SSSR No 17, 1983 | MR

[15] Stanton D., “Orthogonal polynomials and Chevalley groups”, Special Functions: Group Theoretical Aspects and Applications, eds. R. Askey e.a., D. Reidel Publishing Company, 1984, 87–128 | DOI | MR | Zbl

[16] Atakishiyev N.M., Suslov S.K., The Hahn and Meixner polynomials of an imaginary argument and some their applications, PHE 84-12, Zeuthen Preprint, 1984 | MR

[17] Nikiforov A.F., Suslov S.K., Sistemy klassicheskikh ortogonalnykh polinomov diskretnoi peremennoi na neravnomernykh setkakh, Preprint IPM im. M.V. Keldysha AN SSSR No 8, 1985

[18] Gelfand I.M., Minlos R.A., Shapiro 3.Ya., Predstavleniya gruppy vraschenii i gruppy Lorentsa, Fizmatgiz, M., 1958 | MR

[19] Vilenkin N.Ya., Spetsialnye funktsii i teoriya predstavlenii grupp, Nauka, M., 1965 | MR

[20] Smorodinskii Ya.A., Shelepin L.A., “Koeffitsienty Klebsha–Gordana s raznykh storon”, UFN, 106 (1972), 3–45 | DOI | MR

[21] Varshalovich D.A., Moskalev A.I., Khersonskii V.K., Kvantovaya teoriya uglovogo momenta, Nauka. Leningr. otd-nie, L., 1975

[22] Bidenkharn L., Lauk D., Uglovoi moment v kvantovoi fizike, tt. 1, 2, Mir, M., 1984

[23] Koornwinder T.H., “Krawtchouk polynomials, a unification of two different group theoretic interpretations”, SIAM J. Math. Anal., 13 (1982), 1011–1023 | DOI | MR | Zbl

[24] Smirnov Yu.F., Suslov S.K., Shirokov A.M., “Clebsch–Gordan coefficients and Racah coefficients for the $SU(2)$ and $SU(1,1)$ groups as the discrete analogues of the Poschl–Teller potential wave functions”, J. Phys. A: Math. Gen., 17 (1984), 2157–2175 | DOI | MR | Zbl

[25] Koornwinder T.H., “Clebsch–Gordan coefficients for $SU(2)$ and Hahn polynomials”, Nieuw Arch. V. Wisk. (3), XXIX (1981), 140–155 | MR

[26] Smorodinskii Ya.A., Suslov S.K., “Koeffitsienty Klebsha–Gordana gruppy $SU(2)$ i polinomy Khana”, YaF, 35:1 (1982), 192–201 | MR

[27] Nikiforov A.F., Suslov S.K., Polinomy Khana i ikh svyaz s koeffitsientami Klebsha–Gordana gruppy $SU(2)$, Preprint IPM im. M.V. Keldysha AN SSSR No 83, 1982 | MR

[28] Ryvkin V.B., “Predstavlenie koeffitsientov Klebsha–Gordana v vide konechno-raznostnykh analogov polinomov Yakobi”, DAN BSSR, 3 (1959), 183–185 | MR | Zbl

[29] Meckler A., “On the algebra of angular momentum”, Nuovo Gim. Suppl., XII (1959), 1–40 | DOI | MR

[30] Kirichenko I.K., Stepanovskii Yu.P., “«Fizicheskie» form-faktory i kovariantnaya parametrizatsiya elektromagnitnogo toka chastitsy s proizvolnym spinom”, YaF, 20 (1974), 554–561

[31] Nikiforov A.F., Suslov S.K., Uvarov V.B., Asimptoticheskie formuly vtorogo poryadka tochnosti dlya koeffitsientov Klebsha–Gordana i $6j$-simvolov Vignera, Preprint IPM im. M.V. Keldysha AN SSSR No 64, 1983 | MR

[32] Stone A.P., “Some properties of Wigner coefficients and hyperspherical harmonics”, Proc. Cambr. Phil. Soc., 52 (1956), 424–430 | DOI | MR | Zbl

[33] Smorodinskii Ya.A., Suslov S.K., “$6j$-simvoly i ortogonalnye polinomy”, YaF, 36:4(10) (1982), 1066–1071 | MR

[34] Racah G., “Theory of complex spectra I–III”, Phys. Rev., 61 (1941), 186–197 ; 62 (1942), 438–462 ; 63 (1943), 367–382 | DOI | DOI | DOI

[35] Suslov S.K., “$9j$-simvoly kak ortogonalnye polinomy ot dvukh diskretnykh peremennykh”, YaF, 38:10 (1983), 1102–1104 | MR | Zbl

[36] Suslov S.K., “Polinomy Khana v kulonovoi zadache”, YaF, 40:1(7) (1984), 126–132

[37] Suslov S.K., “$T$-koeffitsienty kak ortogonalnye polinomy diskretnoi peremennoi”, YaF, 38:5(11) (1983), 1367–1374 | MR