Asymptotic properties of orthogonal Hahn polynomials in a discrete variable

I. I. Sharapudinov

Sbornik. Mathematics, Tome 68 (1991) no. 1, pp. 111-132

Bibliographie

[1] Chebyshev P. L., Poln. sobr. soch. v 5 t., t. 2, Izd-vo AN SSSR, M., 1947–1951, 236–238, 314–334; т. 3

[2] Hahn W., “Uber orthogonalpolynome, die $q$-Differenzengleihungen genugen”, Math. Nachr., 2 (1949), 4–34 | DOI | MR | Zbl

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

[4] Karlin S., McGregor J. L., “The Hanh polynomials, formulas and an applications”, Scr. Math., 26 (1961), 33–46 | MR | Zbl

[5] Wilson M. W., “On the Hanh polynomials”, SIAM J. Math. Anal., 42:1 (1970), 131–139 | DOI | MR

[6] Gasper G., “Nonnegativity of a discrete Poisson kernel for the Hahn polynomials”, J. Math. Anal. and Appl., 42:2 (1973), 438–451 | DOI | MR | Zbl

[7] Gasper G., “Positivity and special functions”, Theory and Appl. Spec. Funct., Academic Press, New York, 1975, 375–433 | MR

[8] Mizan Rahman, “A generalization of Gasper's kernel for Hahn polynomials: application to Pollaczek polynomials”, Can. J. Math., 30:1 (1978), 133–146 | MR | Zbl

[9] Doge J. C. I., Gervey B. J., “The use of Meixner function in the identification of heavily damped systems”, Proc. of the Roy. Irish Academy, 78:A. 18 (1978), 157–179 | MR

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

[11] Dedus F. F., “Klassicheskie ortogonalnye bazisy diskretnoi peremennoi”, Spektralnye metody obrabotki informatsii v nauchnykh issledovaniyakh, Otd. nauch.-tekhn. inf. nauch. tsentra biologii i selektsii AN SSSR, Puschino, 1980, 21–37

[12] Gabutti B., Minetti B., “A new application of the Hankel transform of a strongly decreasing even function”, J. Comput. Phys., 42:2 (1981), 277–287 | DOI | Zbl

[13] Koornwinder T. H., “Clebsch–Gordon coefficients for $SU(2)$ and Hahn polynomials”, Nieuv Arch. Wisk., 29 (1981), 140–155 | MR | Zbl

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

[15] Askey R., Schonberg I. J., Sharma A., “Hausdorff's Moment Problem and Expansions in Legendre Polynomials”, J. of Math. Anal. and Appl., 86 (1982), 237–245. | DOI | MR | Zbl

[16] Sharapudinov I. I., “Funktsiya Lebega chastnykh summ ryada Fure po polinomam Khana”, Funkts. analiz, teoriya funktsii i ikh prilozheniya, Izd-vo Dag. gos. un-ta, Makhachkala, 1982, 132–144

[17] Sharapudinov I. I., “Nekotorye svoistva mnogochlenov, ortogonalnykh na konechnoi sisteme tochek”, Izv. vuzov. Matematika, no. 5, 1983, 85–88 | MR | Zbl

[18] Sharapudinov I. I., Asimptoticheskie svoistva mnogochlenov Meiksnera i nekotorye ikh prilozheniya, Dep. v VINITI No 1433–83, M., 1983

[19] Sharapudinov I. I., “Vesovye otsenki mnogochlenov Khana”, Teoriya funktsii i priblizhenii., Tr. Saratovskoi zimnei shkoly. Ch. 2 (24 yanvarya–5 fevralya 1982 g.), Izd-vo Sarat. un–ta, Saratov, 1983, 150–154 | MR

[20] Sharapudinov I. I., “Asimptoticheskie svoistva i vesovye otsenki mnogochlenov Khana”, Izv. vuzov. Matematika, 1985, no. 5, 78–80 | MR | Zbl

[21] Sharapudinov I. I., “On the Hahn polynomials application for the optimal tabulation of functions”, Konstruktivnaya teoriya funktsii, Tr. Mezhdunar. konf. po konstruktivnoi teorii funktsii (27 maya–2 iyunya 1984 g.), Sofiya, 1984, 782–787 | Zbl

[22] Sharapudinov I. I., “O primenenii mnogochlenov Meiksnera k priblizhennomu vychisleniyu integralov”, Izv. vuzov. Matematika, 1986, no. 2, 80–82 | MR | Zbl

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

[24] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, T. 1, 2, Nauka, M., 1973, 1974

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

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

[27] Bernshtein S. N., “O mnogochlenakh, ortogonalnykh na konechnom otrezke”, Poln. sobr. soch., t. 2, Izd. AN SSSR, M., 1954, 7–106