메뉴 건너뛰기




Volumn 49, Issue 3, 1997, Pages 520-542

Classical orthogonal polynomials as moments

Author keywords

Al Salam Chihara polynomials; Classical orthogonal polynomials; Continuous q ultraspherical polynomials; Generating functions; Multilinear generating functions; Transformation formulas; Umbral calculus

Indexed keywords


EID: 0031519781     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-1997-024-9     Document Type: Article
Times cited : (52)

References (31)
  • 1
    • 84966219999 scopus 로고
    • Some orthogonal q-polynomials
    • W.A. Al-Salam and L. Carlitz, Some orthogonal q-polynomials, Math. Nachr. 30(1965), 47-61.
    • (1965) Math. Nachr. , vol.30 , pp. 47-61
    • Al-Salam, W.A.1    Carlitz, L.2
  • 2
  • 3
    • 0040152154 scopus 로고
    • On the foundations of combinatorial theory, V: Eulerian differential operators
    • G. E. Andrews, On the foundations of combinatorial theory, V: Eulerian differential operators, Stud. Appl. Math. 50(1971), 345-375.
    • (1971) Stud. Appl. Math. , vol.50 , pp. 345-375
    • Andrews, G.E.1
  • 4
    • 0001683859 scopus 로고
    • Classical orthogonal polynomials
    • Polynomes Orthogonaux et Applications, (eds. C. Brezinski et ál.), Springer-Verlag, Berlin
    • G. E. Andrews and R. A. Askey, Classical orthogonal polynomials. In: Polynomes Orthogonaux et Applications, (eds. C. Brezinski et ál.), Lecture Notes in Math. 1171, Springer-Verlag, Berlin, 1984, 36-63.
    • (1984) Lecture Notes in Math. , vol.1171 , pp. 36-63
    • Andrews, G.E.1    Askey, R.A.2
  • 5
    • 0001404363 scopus 로고
    • Recurrence relations, continued fractions and orthogonal polynomials
    • R. A. Askey and M. E. H. Ismail, Recurrence relations, continued fractions and orthogonal polynomials, Mem. Amer. Math. Soc. 300(1984).
    • (1984) Mem. Amer. Math. Soc. , vol.300
    • Askey, R.A.1    Ismail, M.E.H.2
  • 6
    • 0030123811 scopus 로고    scopus 로고
    • On a general q-Fourier transformation with nonsymmetric kernels
    • R. A. Askey, M. Rahman, and S. K. Suslov, On a general q-Fourier transformation with nonsymmetric kernels, J. Comput. Appl. Math. 68(1996), 25-55.
    • (1996) J. Comput. Appl. Math. , vol.68 , pp. 25-55
    • Askey, R.A.1    Rahman, M.2    Suslov, S.K.3
  • 7
    • 0001308382 scopus 로고
    • Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
    • R. A. Askey and J. A. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 319(1985).
    • (1985) Mem. Amer. Math. Soc. , vol.319
    • Askey, R.A.1    Wilson, J.A.2
  • 8
    • 0030543222 scopus 로고    scopus 로고
    • q-Hermite polynomials and the classical polynomials
    • C. Berg and M. E. H. Ismail, q-Hermite polynomials and the classical polynomials, Canad. J. Math. 48(1996), 43-63.
    • (1996) Canad. J. Math. , vol.48 , pp. 43-63
    • Berg, C.1    Ismail, M.E.H.2
  • 13
    • 84891696012 scopus 로고
    • Positively of the Poisson kernel for the continuous q-ultraspherical polynomials
    • _, Positively of the Poisson kernel for the continuous q-ultraspherical polynomials, SIAM J. Math. Anal. 14(1983), 409-420.
    • (1983) SIAM J. Math. Anal. , vol.14 , pp. 409-420
  • 14
    • 38249008207 scopus 로고
    • Contiguous relations, basic hypergeometric functions and orthogonal polynomials. II: Associated big q-Jacobi polynomials
    • D. P. Gupta, M. E. H. Ismail and D. R. Masson, Contiguous relations, basic hypergeometric functions and orthogonal polynomials. II: Associated big q-Jacobi polynomials, J. Math. Anal. Appl. 171(1993), 477-497.
    • (1993) J. Math. Anal. Appl. , vol.171 , pp. 477-497
    • Gupta, D.P.1    Ismail, M.E.H.2    Masson, D.R.3
  • 17
    • 0031490225 scopus 로고    scopus 로고
    • Some summation theorems and transformation formulas for q-series
    • M. E. H. Ismail, M. Rahman and S. K. Suslov, Some summation theorems and transformation formulas for q-series, Canad. J. Math. 49(1997), 543-567.
    • (1997) Canad. J. Math. , vol.49 , pp. 543-567
    • Ismail, M.E.H.1    Rahman, M.2    Suslov, S.K.3
  • 18
    • 0000083862 scopus 로고
    • On the Askey-Wilson and Rogers polynomials
    • M. E. H. Ismail and D. Stanton, On the Askey-Wilson and Rogers polynomials, Canad. J. Math. 40(1988), 1025-1045.
    • (1988) Canad. J. Math. , vol.40 , pp. 1025-1045
    • Ismail, M.E.H.1    Stanton, D.2
  • 19
    • 0002738602 scopus 로고
    • Coalgebras and bialgebras in combinatorics
    • S. A. Joni and G. C. Rota, Coalgebras and bialgebras in combinatorics, Stud. Appl. Math. 61(1978), 93-139.
    • (1978) Stud. Appl. Math. , vol.61 , pp. 93-139
    • Joni, S.A.1    Rota, G.C.2
  • 20
    • 85033082513 scopus 로고
    • Sign regularity of classical orthogonal polynomials
    • (ed. D. Haimo), Southern Illinois Univ. Press, Carbondale
    • S. Karlin, Sign regularity of classical orthogonal polynomials. In: Orthogonal Expansions and Their Continuous Analogues, (ed. D. Haimo), Southern Illinois Univ. Press, Carbondale, 1967, 55-74.
    • (1967) Orthogonal Expansions and Their Continuous Analogues , pp. 55-74
    • Karlin, S.1
  • 21
    • 0041152004 scopus 로고
    • An extension of theorem of Mehler on Hermite polynomials
    • W.F. Kibble, An extension of theorem of Mehler on Hermite polynomials, Math. Proc. Cambridge Philos. Soc. 41(1945), 12-15.
    • (1945) Math. Proc. Cambridge Philos. Soc. , vol.41 , pp. 12-15
    • Kibble, W.F.1
  • 22
    • 0009122874 scopus 로고
    • Unformung gewisser reihen, deren gleider produkte hypergeometrischer funktionen sind
    • J. Meixner, Unformung gewisser Reihen, deren Gleider Produkte hypergeometrischer Funktionen sind, Deutsch. Math. 6(1942), 341-349.
    • (1942) Deutsch. Math. , vol.6 , pp. 341-349
    • Meixner, J.1
  • 24
    • 0039964921 scopus 로고
    • A generalization of Gasper's kernel for Hahn polynomials: Application to Pollaczek polynomials
    • M. Rahman, A generalization of Gasper's kernel for Hahn polynomials: application to Pollaczek polynomials. Canad. J. Math. 30(1988), 133-146.
    • (1988) Canad. J. Math. , vol.30 , pp. 133-146
    • Rahman, M.1
  • 25
    • 0012276749 scopus 로고
    • A q-integral representation for the Rogers q-ultraspherical polynomials and some applications
    • M. Rahman and A. Verma, A q-integral representation for the Rogers q-ultraspherical polynomials and some applications. Constr. Approx. 2(1986), 1-10.
    • (1986) Constr. Approx. , vol.2 , pp. 1-10
    • Rahman, M.1    Verma, A.2
  • 26
    • 0002300455 scopus 로고
    • The umbral calculus
    • S. Roman and G. C. Rota, The umbral calculus, Adv. in Math. 27(1978), 95-188.
    • (1978) Adv. in Math. , vol.27 , pp. 95-188
    • Roman, S.1    Rota, G.C.2
  • 27
    • 0007259725 scopus 로고
    • On the symmetrized Kronecker power of a matrix and extensions of Mehler's formula for Hermite polynomials
    • D. Slepian, On the symmetrized Kronecker power of a matrix and extensions of Mehler's formula for Hermite polynomials, SIAM J. Math. Anal. 3(1972), 606-616.
    • (1972) SIAM J. Math. Anal. , vol.3 , pp. 606-616
    • Slepian, D.1
  • 28
    • 85033097172 scopus 로고    scopus 로고
    • unpublished notes
    • S. K. Suslov, unpublished notes.
    • Suslov, S.K.1
  • 31
    • 0039648140 scopus 로고
    • Some explicit Pade approximates for the function Φ′/Φ and a related quadrature formula involving Bessel functions
    • J. Wimp, Some explicit Pade approximates for the function Φ′/Φ and a related quadrature formula involving Bessel functions, SIAM J. Math. Anal. 16(1985), 887-896.
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 887-896
    • Wimp, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.