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Volumn 99, Issue 1-2, 1998, Pages 77-89

Strong asymptotics for Laguerre polynomials with varying weights

Author keywords

Laguerre polynomials; Plancherel Rotach formulae; Strong asymptotics

Indexed keywords

ASYMPTOTIC STABILITY; FUNCTIONS; INTEGRAL EQUATIONS; PROBLEM SOLVING;

EID: 0032207908     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(98)00147-2     Document Type: Article
Times cited : (17)

References (30)
  • 2
    • 0000891997 scopus 로고
    • On asymptotics of jacobi polynomials
    • L.-C. Chen, M.E.H. Ismail, On asymptotics of Jacobi polynomials, SIAM J. Math. Anal. 22 (1991) 1442-1449.
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1442-1449
    • Chen, L.-C.1    Ismail, M.E.H.2
  • 3
    • 38249008558 scopus 로고
    • On a new characterization of the classical orthogonal polynomials
    • H. Dette, W.J. Studden, On a new characterization of the classical orthogonal polynomials, J. Approx. Theory 71 (1992) 3-17.
    • (1992) J. Approx. Theory , vol.71 , pp. 3-17
    • Dette, H.1    Studden, W.J.2
  • 4
    • 21844504037 scopus 로고
    • Some new asymptotic properties for the zeros of Jacobi, Laguerre and Hermite polynomials
    • H. Dette, W.J. Studden, Some new asymptotic properties for the zeros of Jacobi, Laguerre and Hermite polynomials, Constr. Approx. 11 (1995) 227-238.
    • (1995) Constr. Approx. , vol.11 , pp. 227-238
    • Dette, H.1    Studden, W.J.2
  • 5
    • 0000577465 scopus 로고
    • Uniform asymptotic expansions for Whittaker's confluent hypergeometric functions
    • T.M. Dunster, Uniform asymptotic expansions for Whittaker's confluent hypergeometric functions, SIAM J. Math. Anal. 20 (1989) 744-760.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 744-760
    • Dunster, T.M.1
  • 6
    • 0000383297 scopus 로고
    • Asymptotic forms for Laguerre polynomials
    • A. Erdelyi, Asymptotic forms for Laguerre polynomials, J. Ind. Math. Soc. 24 (1960) 235-250.
    • (1960) J. Ind. Math. Soc. , vol.24 , pp. 235-250
    • Erdelyi, A.1
  • 7
    • 0001684607 scopus 로고
    • On the limit distributions of the zeros of Jonquière polynomials and generalized classical orthogonal polynomials
    • J. Faldey, W. Gawronski, On the limit distributions of the zeros of Jonquière polynomials and generalized classical orthogonal polynomials, J. Approx. Theory 81 (1995) 231-249.
    • (1995) J. Approx. Theory , vol.81 , pp. 231-249
    • Faldey, J.1    Gawronski, W.2
  • 8
    • 0000093146 scopus 로고
    • Uniform asymptotic expansions for Laguerre polynomials
    • C.L. Frenzen, R. Wong, Uniform asymptotic expansions for Laguerre polynomials, SIAM J. Math. Anal. 19 (1988) 1232-1248.
    • (1988) SIAM J. Math. Anal. , vol.19 , pp. 1232-1248
    • Frenzen, C.L.1    Wong, R.2
  • 9
    • 38249035482 scopus 로고
    • On the asymptotic distribution of the zeros of Hermite, Laguerre and Jonquière polynomials
    • W. Gawronski, On the asymptotic distribution of the zeros of Hermite, Laguerre and Jonquière polynomials, J. Approx. Theory 50 (1987) 214-231.
    • (1987) J. Approx. Theory , vol.50 , pp. 214-231
    • Gawronski, W.1
  • 11
    • 0011531994 scopus 로고
    • On convergence of simultaneous Padé approximants for systems of Markov type
    • A.A. Gonchar, E.A. Rakhmanov, On convergence of simultaneous Padé approximants for systems of Markov type, Proc. Steklov Inst. Math. 157 (1983) 31-50.
    • (1983) Proc. Steklov Inst. Math. , vol.157 , pp. 31-50
    • Gonchar, A.A.1    Rakhmanov, E.A.2
  • 12
    • 84956094024 scopus 로고
    • Equilibrium measure and the distribution of zeros of extremal polynomials
    • A.A. Gonchar, E.A. Rakhmanov, Equilibrium measure and the distribution of zeros of extremal polynomials, Math. USSR Sbornik 53 (1986) 119-130.
    • (1986) Math. USSR Sbornik , vol.53 , pp. 119-130
    • Gonchar, A.A.1    Rakhmanov, E.A.2
  • 14
    • 0000625846 scopus 로고
    • A survey of general orthogonal polynomials for weights on finite and infinite intervals
    • D.S. Lubinsky, A survey of general orthogonal polynomials for weights on finite and infinite intervals, Acta Appl. Math. 10 (1987) 237-296.
    • (1987) Acta Appl. Math. , vol.10 , pp. 237-296
    • Lubinsky, D.S.1
  • 17
    • 84968466269 scopus 로고
    • Weighted polynomials on finite and infinite intervals: A unified approach
    • H.N. Mhaskar, E.B. Saff, Weighted polynomials on finite and infinite intervals: a unified approach, Bull. Amer. Math. Soc. 11 (1984) 351-354.
    • (1984) Bull. Amer. Math. Soc. , vol.11 , pp. 351-354
    • Mhaskar, H.N.1    Saff, E.B.2
  • 19
    • 0002534477 scopus 로고
    • Where does the sup norm of a weighted polynomial live? (a generalization of incomplete polynomials)
    • H.N. Mhaskar, E.B. Saff, Where does the sup norm of a weighted polynomial live? (A generalization of incomplete polynomials), Constr. Approx. 1 (1985) 71-91.
    • (1985) Constr. Approx. , vol.1 , pp. 71-91
    • Mhaskar, H.N.1    Saff, E.B.2
  • 20
    • 0000956929 scopus 로고
    • Orthogonal polynomials
    • Providence, RI
    • P. Nevai, Orthogonal Polynomials, vol. 213 of Memoirs Amer. Math. Soc., Providence, RI, 1979.
    • (1979) Memoirs Amer. Math. Soc. , vol.213
    • Nevai, P.1
  • 22
    • 0002199842 scopus 로고
    • Strong asymptotics for orthogonal polynomials
    • Methods of Approximation Theory in Complex Analysis and Mathematical Physics, A.A. Gonchar, E.B. Saff (eds.), Springer, Berlin
    • E.A. Rakhmanov, Strong asymptotics for orthogonal polynomials, in: Methods of Approximation Theory in Complex Analysis and Mathematical Physics, A.A. Gonchar, E.B. Saff (eds.), Lecture Notes in Mathematics, vol. 1550, Springer, Berlin, 1993, pp. 71-97.
    • (1993) Lecture Notes in Mathematics , vol.1550 , pp. 71-97
    • Rakhmanov, E.A.1
  • 23
    • 0038780347 scopus 로고
    • The sharpness of Lorentz's theorem on incomplete polynomials
    • E.B. Saff, R.S. Varga, The sharpness of Lorentz's theorem on incomplete polynomials, Trans. Amer. Math. Soc. 249 (1979) 163-186.
    • (1979) Trans. Amer. Math. Soc. , vol.249 , pp. 163-186
    • Saff, E.B.1    Varga, R.S.2
  • 24
    • 0003217929 scopus 로고
    • Orthogonal polynomials
    • Providence, RI
    • G. Szegö, Orthogonal Polynomials, Amer. Math. Soc., Providence, RI, 1975.
    • (1975) Amer. Math. Soc.
    • Szegö, G.1
  • 25
    • 0000268177 scopus 로고
    • Asymptotic estimates for Laguerre polynomials
    • N. Temme, Asymptotic estimates for Laguerre polynomials, J. Appl. Math. Phys. 41 (1990) 114-126.
    • (1990) J. Appl. Math. Phys. , vol.41 , pp. 114-126
    • Temme, N.1
  • 26
    • 0039964235 scopus 로고
    • Polynomial asymptotic estimates of Gegenbauer, Laguerre and Jacobi polynomials
    • Asymptotic and Computational Analysis, Proc., R. Wong (ed.), Dekker, New York
    • N. Temme, Polynomial asymptotic estimates of Gegenbauer, Laguerre and Jacobi polynomials, in: Asymptotic and Computational Analysis, Proc., R. Wong (ed.), Lect. Notes Pure Appl. Math. 124, Dekker, New York, 1990, pp. 455-476.
    • (1990) Lect. Notes Pure Appl. Math. , vol.124 , pp. 455-476
    • Temme, N.1
  • 28
    • 0003190396 scopus 로고
    • Some recent results on the asymptotic distribution of the zeros of orthogonal ploynomials
    • W. Van Assche, Some recent results on the asymptotic distribution of the zeros of orthogonal ploynomials, J. Comput. Appl. Math. 12 & 13 (1985) 615-623.
    • (1985) J. Comput. Appl. Math. , vol.12-13 , pp. 615-623
    • Van Assche, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.