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Volumn 196, Issue 1, 2006, Pages 320-337

On characterizations of classical polynomials

Author keywords

Characterization theorems; Classical polynomials; Discrete polynomials; q Hahn tableau

Indexed keywords

BESSEL FUNCTIONS; DIFFERENCE EQUATIONS; DIFFERENTIATION (CALCULUS); EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL TECHNIQUES; PROBLEM SOLVING;

EID: 33745891556     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.06.046     Document Type: Article
Times cited : (59)

References (28)
  • 1
    • 0002803522 scopus 로고
    • Characterization theorems for orthogonal polynomials
    • Nevai P. (Ed), Kluwer Academic Publisher, Dordrecht
    • Al-Salam W.A. Characterization theorems for orthogonal polynomials. In: Nevai P. (Ed). Orthogonal Polynomials: Theory and Practice, NATO ASI Series C vol. 294 (1990), Kluwer Academic Publisher, Dordrecht 1-24
    • (1990) Orthogonal Polynomials: Theory and Practice, NATO ASI Series C , vol.294 , pp. 1-24
    • Al-Salam, W.A.1
  • 2
    • 0002718586 scopus 로고
    • Another characterization of the classical orthogonal polynomials
    • Al-Salam W.A., and Chihara T.S. Another characterization of the classical orthogonal polynomials. SIAM J. Math. Anal. 3 (1972) 65-70
    • (1972) SIAM J. Math. Anal. , vol.3 , pp. 65-70
    • Al-Salam, W.A.1    Chihara, T.S.2
  • 3
    • 33745913829 scopus 로고    scopus 로고
    • R. Álvarez-Nodarse, Polinomios hipergeométricos y q-polinomios. Monografías del Seminario Matemático "García de Galdeano", vol. 26. Prensas Universitarias de Zaragoza, Zaragoza, Spain, 2003 (in Spanish).
  • 5
    • 0035888122 scopus 로고    scopus 로고
    • q-Classical polynomials and the q-Askey and Nikiforov-Uvarov Tableaus
    • Álvarez-Nodarse R., and Medem J.C. q-Classical polynomials and the q-Askey and Nikiforov-Uvarov Tableaus. J. Comput. Appl. Math. 135 (2001) 197-223
    • (2001) J. Comput. Appl. Math. , vol.135 , pp. 197-223
    • Álvarez-Nodarse, R.1    Medem, J.C.2
  • 7
    • 0000032737 scopus 로고
    • Über Sturm-Liouvillesche polynomsysteme
    • Bochner S. Über Sturm-Liouvillesche polynomsysteme. Math. Z. 29 (1929) 730-736
    • (1929) Math. Z. , vol.29 , pp. 730-736
    • Bochner, S.1
  • 9
    • 0003358801 scopus 로고
    • Rodrigues' formula and the classical orthogonal polynomials
    • Cryer C.W. Rodrigues' formula and the classical orthogonal polynomials. Boll. Un. Mat. Ital. 25 3 (1970) 1-11
    • (1970) Boll. Un. Mat. Ital. , vol.25 , Issue.3 , pp. 1-11
    • Cryer, C.W.1
  • 10
    • 0001221148 scopus 로고
    • A distributional study of discrete classical orthogonal polynomials
    • García A.G., Marcellán F., and Salto L. A distributional study of discrete classical orthogonal polynomials. J. Comput. Appl. Math. 57 (1995) 147-162
    • (1995) J. Comput. Appl. Math. , vol.57 , pp. 147-162
    • García, A.G.1    Marcellán, F.2    Salto, L.3
  • 12
    • 0001372628 scopus 로고
    • Über die Jacobischen polynome und zwei verwandte polynomklassen
    • Hahn W. Über die Jacobischen polynome und zwei verwandte polynomklassen. Math. Z. 39 (1935) 634-638
    • (1935) Math. Z. , vol.39 , pp. 634-638
    • Hahn, W.1
  • 13
    • 0003124908 scopus 로고
    • Über orthogonalpolynomen die q-differentialgleichungen genügen
    • Hahn W. Über orthogonalpolynomen die q-differentialgleichungen genügen. Math. Nachr. 2 (1949) 4-34
    • (1949) Math. Nachr. , vol.2 , pp. 4-34
    • Hahn, W.1
  • 14
    • 0000007742 scopus 로고
    • Systems of polynomials connected with the Charlier expansion and the Pearson differential and difference equation
    • Hildebrandt E.H. Systems of polynomials connected with the Charlier expansion and the Pearson differential and difference equation. Ann. Math. Statist. 2 (1931) 379-439
    • (1931) Ann. Math. Statist. , vol.2 , pp. 379-439
    • Hildebrandt, E.H.1
  • 15
    • 33745905212 scopus 로고    scopus 로고
    • R. Koekoek, R.F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analog, Reports of the Faculty of Technical Mathematics and Informatics, vol. 98-17. Delft University of Technology, Delft, 1998.
  • 16
    • 33745930411 scopus 로고    scopus 로고
    • T.H. Koornwinder, Compact quantum groups and q-special functions, in: V. Baldoni, M.A. Picardello (Eds.), Representations of Lie Groups and Quantum Groups. Pitman Research Notes in Mathematics Series 311, Longman Scientific & Technical, 1994, New York, 46-128.
  • 17
    • 0000366446 scopus 로고
    • Über Polynomsysteme die Sturm-Liouvilleschen differenzengleichungen genügen
    • Lesky P. Über Polynomsysteme die Sturm-Liouvilleschen differenzengleichungen genügen. Math. Z. 78 (1962) 439-445
    • (1962) Math. Z. , vol.78 , pp. 439-445
    • Lesky, P.1
  • 19
    • 0000672705 scopus 로고
    • Classical orthogonal polynomials: a functional approach
    • Marcellán F., Branquinho A., and Petronilho J. Classical orthogonal polynomials: a functional approach. Acta Appl. Math. 34 (1994) 283-303
    • (1994) Acta Appl. Math. , vol.34 , pp. 283-303
    • Marcellán, F.1    Branquinho, A.2    Petronilho, J.3
  • 20
    • 21444441335 scopus 로고
    • On the solution of some distributional differential equations: existence and characterizations of the classical moment functionals
    • Marcellán F., and Petronilho J. On the solution of some distributional differential equations: existence and characterizations of the classical moment functionals. Integral Transform. Special Funct. 2 (1994) 185-218
    • (1994) Integral Transform. Special Funct. , vol.2 , pp. 185-218
    • Marcellán, F.1    Petronilho, J.2
  • 21
    • 0036980532 scopus 로고    scopus 로고
    • The quasi-orthogonality of the derivatives of semi-classical polynomials
    • Medem J.C. The quasi-orthogonality of the derivatives of semi-classical polynomials. Indag. Math. New Ser. 13 (2002) 363-387
    • (2002) Indag. Math. New Ser. , vol.13 , pp. 363-387
    • Medem, J.C.1
  • 22
    • 0036980564 scopus 로고    scopus 로고
    • A family of singular semi-classical functionals
    • Medem J.C. A family of singular semi-classical functionals. Indag. Math. New Ser. 13 (2002) 351-362
    • (2002) Indag. Math. New Ser. , vol.13 , pp. 351-362
    • Medem, J.C.1
  • 26
    • 0000673373 scopus 로고
    • Polynomial solutions of hypergeometric type difference equations and their classification
    • Nikiforov A.F., and Uvarov V.B. Polynomial solutions of hypergeometric type difference equations and their classification. Integral Transform. Special Funct. 1 (1993) 223-249
    • (1993) Integral Transform. Special Funct. , vol.1 , pp. 223-249
    • Nikiforov, A.F.1    Uvarov, V.B.2
  • 27
    • 0003201549 scopus 로고
    • The theory of difference analogues of special functions of hypergeometric type
    • (English translation Russian Math. Surveys 44(2) (1989) 227-278)
    • Suslov S.K. The theory of difference analogues of special functions of hypergeometric type. Uspekhi Mat. Nauk. 44 2 (1989) 185-226 (English translation Russian Math. Surveys 44(2) (1989) 227-278)
    • (1989) Uspekhi Mat. Nauk. , vol.44 , Issue.2 , pp. 185-226
    • Suslov, S.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.