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Volumn 54, Issue 1, 1998, Pages 27-58

WKB Approximation and Krall-Type Orthogonal Polynomials

Author keywords

Distribution of zeros; Krall type polynomials; Tridiagonal matrices; WKB approximation

Indexed keywords


EID: 2342512373     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006006519197     Document Type: Article
Times cited : (14)

References (47)
  • 2
    • 0000298599 scopus 로고
    • Difference equation for modification of Meixner polynomials
    • Álvarez-Nodarse, R. and Marcellán, F.: Difference equation for modification of Meixner polynomials, J. Math. Anal. Appl. 194(3) (1995), 250-258.
    • (1995) J. Math. Anal. Appl. , vol.194 , Issue.3 , pp. 250-258
    • Álvarez-Nodarse, R.1    Marcellán, F.2
  • 3
    • 0002572215 scopus 로고
    • On the properties for modifications of classical orthogonal polynomials of discrete variables
    • Álvarez-Nodarse, R., García, A. G. and Marcellán, F.: On the properties for modifications of classical orthogonal polynomials of discrete variables, J. Comput. Appl. Math. 65 (1995), 3-18.
    • (1995) J. Comput. Appl. Math. , vol.65 , pp. 3-18
    • Álvarez-Nodarse, R.1    García, A.G.2    Marcellán, F.3
  • 4
    • 0000034155 scopus 로고
    • The modification of classical Hahn polynomials of a discrete variable
    • Álvarez-Nodarse, R. and Marcellán, F.: The modification of classical Hahn polynomials of a discrete variable, Integral Transform. Spec. Funct. 4(4) (1995), 243-262.
    • (1995) Integral Transform. Spec. Funct. , vol.4 , Issue.4 , pp. 243-262
    • Álvarez-Nodarse, R.1    Marcellán, F.2
  • 5
    • 0031590241 scopus 로고    scopus 로고
    • The limit relations between generalized orthogonal polynomials
    • Álvarez-Nodarse, R. and Marcellán, F.: The limit relations between generalized orthogonal polynomials, Indag. Mathem. N.S. 8 (1997), 295-316.
    • (1997) Indag. Mathem. N.S. , vol.8 , pp. 295-316
    • Álvarez-Nodarse, R.1    Marcellán, F.2
  • 6
    • 0042160995 scopus 로고    scopus 로고
    • On the modifications of classical orthogonal polynomials: The symmetric case
    • Álvarez-Nodarse, R. and Marcellán, F.: On the modifications of classical orthogonal polynomials: The symmetric case, Approx. Theory Appl. (N.S.) 14(1) (1998), 8-28.
    • (1998) Approx. Theory Appl. (N.S.) , vol.14 , Issue.1 , pp. 8-28
    • Álvarez-Nodarse, R.1    Marcellán, F.2
  • 7
    • 2342469823 scopus 로고    scopus 로고
    • On some polynomial mappings for measures. Applications
    • M. Alfaro et al. (eds), Servicio de Publicaciones de la Universidad Carlos III de Madrid, Leganés
    • Álvarez-Nodarse, R., Marcellán, F. and Petronilho, J.: On some polynomial mappings for measures. Applications, in: M. Alfaro et al. (eds), Proc. Internat. Workshop on Orthogonal Polynomials in Mathematical Physics, Servicio de Publicaciones de la Universidad Carlos III de Madrid, Leganés, 1997, pp. 1-21.
    • (1997) Proc. Internat. Workshop on Orthogonal Polynomials in Mathematical Physics , pp. 1-21
    • Álvarez-Nodarse, R.1    Marcellán, F.2    Petronilho, J.3
  • 8
    • 0009847987 scopus 로고
    • Spectral properties of the biconfluent Heun differential equation
    • Arriola, E. R., Zarzo, A. and Dehesa, J. S.: Spectral properties of the biconfluent Heun differential equation, J. Comput. Appl. Math. 37 (1991), 161-169.
    • (1991) J. Comput. Appl. Math. , vol.37 , pp. 161-169
    • Arriola, E.R.1    Zarzo, A.2    Dehesa, J.S.3
  • 9
    • 38149146625 scopus 로고
    • Difference equations for generalized Meixner polynomials
    • Bavinck, H. and van Haeringen, H.: Difference equations for generalized Meixner polynomials, J. Math. Anal. Appl. 184(3) (1994), 453-463.
    • (1994) J. Math. Anal. Appl. , vol.184 , Issue.3 , pp. 453-463
    • Bavinck, H.1    Van Haeringen, H.2
  • 10
    • 0000149930 scopus 로고
    • On a difference equation for generalizations of Charlier polynomials
    • Bavinck, H. and Koekoek, R.: On a difference equation for generalizations of Charlier polynomials, J. Approx. Theory 81 (1995), 195-206.
    • (1995) J. Approx. Theory , vol.81 , pp. 195-206
    • Bavinck, H.1    Koekoek, R.2
  • 11
    • 0040872562 scopus 로고
    • On the the polynomial solution of ordinary differential equations of the fourth order
    • Buendía, E., Dehesa, S. J. and Sánchez Buendía, M. A.: On the the polynomial solution of ordinary differential equations of the fourth order, J. Math. Phys. 26 (1985), 1547-1552.
    • (1985) J. Math. Phys. , vol.26 , pp. 1547-1552
    • Buendía, E.1    Dehesa, S.J.2    Sánchez Buendía, M.A.3
  • 12
    • 0004413787 scopus 로고
    • The distribution of the zeros of the polynomial eigenfunction of ordinary differential operators of arbitrary order
    • M. Alfaro et al. (eds), Lecture Notes in Mathematics 1329, Springer-Verlag, Berlin
    • Buendía, E., Dehesa, S. J. and Gálvez, F. J.: The distribution of the zeros of the polynomial eigenfunction of ordinary differential operators of arbitrary order, in: M. Alfaro et al. (eds), Orthogonal Polynomials and their Applications, Lecture Notes in Mathematics 1329, Springer-Verlag, Berlin, 1988, pp. 222-235.
    • (1988) Orthogonal Polynomials and Their Applications , pp. 222-235
    • Buendía, E.1    Dehesa, S.J.2    Gálvez, F.J.3
  • 13
    • 0000235008 scopus 로고
    • Orthogonal polynomials and measures with end point masses
    • Chihara, T. S.: Orthogonal polynomials and measures with end point masses, Rocky Mountain J. Math. 15(3) (1985), 705-719.
    • (1985) Rocky Mountain J. Math. , vol.15 , Issue.3 , pp. 705-719
    • Chihara, T.S.1
  • 16
    • 0002994425 scopus 로고
    • Sur l'adjonction de deux masses de Dirac à une forme régulière quelconque
    • A. Cachafeiro and E. Godoy (eds), Actas del V Simposium, Universidad de Santiago, Vigo
    • Draïdi, N. and Maroni, P.: Sur l'adjonction de deux masses de Dirac à une forme régulière quelconque, in: A. Cachafeiro and E. Godoy (eds), Polinomios ortogonales y sus aplicaciones, Actas del V Simposium, Universidad de Santiago, Vigo 1988, pp. 83-90.
    • (1988) Polinomios Ortogonales y sus Aplicaciones , pp. 83-90
    • Draïdi, N.1    Maroni, P.2
  • 17
    • 2342462112 scopus 로고
    • Remark on band matrices
    • Elsner, L. and Redheffer, R. M.: Remark on band matrices, Numer. Math. 10 (1967), 153-161.
    • (1967) Numer. Math. , vol.10 , pp. 153-161
    • Elsner, L.1    Redheffer, R.M.2
  • 21
    • 21344496941 scopus 로고
    • The eigenproblem of a tridiagonal 2-Toeplitz matrix
    • Gover, M. J. C.: The eigenproblem of a tridiagonal 2-Toeplitz matrix, Linear Algebra Appl. 197-198 (1994), 63-78.
    • (1994) Linear Algebra Appl. , vol.197-198 , pp. 63-78
    • Gover, M.J.C.1
  • 23
    • 0001437854 scopus 로고
    • On a differential equation for Koornwinder's generalized Laguerre polynomials
    • Koekoek, J. and Koekoek, R.: On a differential equation for Koornwinder's generalized Laguerre polynomials, Proc. Amer. Math. Soc. 112 (1991), 1045-1054.
    • (1991) Proc. Amer. Math. Soc. , vol.112 , pp. 1045-1054
    • Koekoek, J.1    Koekoek, R.2
  • 24
    • 21144479788 scopus 로고
    • A generalization of Laguerre polynomials
    • Koekoek, R. and Meijer, H. G.: A generalization of Laguerre polynomials, SIAM J. Math. Anal. 24(3) (1993), 768-782.
    • (1993) SIAM J. Math. Anal. , vol.24 , Issue.3 , pp. 768-782
    • Koekoek, R.1    Meijer, H.G.2
  • 25
    • 0001291496 scopus 로고
    • Koornwinder's Laguerre polynomials
    • Koekoek, R.: Koornwinder's Laguerre polynomials, Delft Progress Report 12 (1988), 393-404.
    • (1988) Delft Progress Report , vol.12 , pp. 393-404
    • Koekoek, R.1
  • 26
    • 0003056965 scopus 로고
    • Differential equations for symmetric generalized ultraspherical polynomials
    • Koekoek, R.: Differential equations for symmetric generalized ultraspherical polynomials, Trans. Amer. Math. Soc. 345 (1994), 47-72.
    • (1994) Trans. Amer. Math. Soc. , vol.345 , pp. 47-72
    • Koekoek, R.1
  • 28
    • 2342598237 scopus 로고
    • A package on formal power series
    • Koepf, W.: A package on formal power series, Mathematica 4(2) (1994), 62-69.
    • (1994) Mathematica , vol.4 , Issue.2 , pp. 62-69
    • Koepf, W.1
  • 29
    • 0000879648 scopus 로고
    • β + Mδ(x + 1) + Nδ(x - 1)
    • β + Mδ(x + 1) + Nδ(x - 1), Canad. Math. Bull. 27(2) (1984), 205-214.
    • (1984) Canad. Math. Bull. , vol.27 , Issue.2 , pp. 205-214
    • Koornwinder, T.H.1
  • 30
    • 84971195130 scopus 로고
    • Orthogonal polynomials satisfying fourth order differential equations
    • Krall, A. M.: Orthogonal polynomials satisfying fourth order differential equations, Proc. Roy. Soc. Edinburgh 87 (1981), 271-288.
    • (1981) Proc. Roy. Soc. Edinburgh , vol.87 , pp. 271-288
    • Krall, A.M.1
  • 31
    • 0003272555 scopus 로고
    • On orthogonal polynomials satisfying a certain fourth order differential equation
    • Krall, H. L.: On orthogonal polynomials satisfying a certain fourth order differential equation, The Pennsylvania State College Bulletin 6 (1940), 1-24.
    • (1940) The Pennsylvania State College Bulletin , vol.6 , pp. 1-24
    • Krall, H.L.1
  • 32
    • 0031584991 scopus 로고    scopus 로고
    • Two points masses perturbation of regular moment functionals
    • Kwon, H. K. and Park, S. B.: Two points masses perturbation of regular moment functionals, Indag. Math. (N.S.) 8 (1997), 79-94.
    • (1997) Indag. Math. (N.S.) , vol.8 , pp. 79-94
    • Kwon, H.K.1    Park, S.B.2
  • 33
    • 0000295908 scopus 로고
    • The Krall polynomials: A new class of orthogonal polynomials
    • Littlejohn, L. L.: The Krall polynomials: A new class of orthogonal polynomials, Quaestiones Math. 5 (1982), 255-265.
    • (1982) Quaestiones Math. , vol.5 , pp. 255-265
    • Littlejohn, L.L.1
  • 34
    • 0002379502 scopus 로고
    • Sur l'adjonction d'une masse de Dirac à une forme régulière et semi-classique
    • Marcellán, F. and Maroni, P: Sur l'adjonction d'une masse de Dirac à une forme régulière et semi-classique, Ann. Mat. Pura Appl. IV, CLXII (1992), 1-22.
    • (1992) Ann. Mat. Pura Appl. IV , vol.162 , pp. 1-22
    • Marcellán, F.1    Maroni, P.2
  • 35
    • 0042627852 scopus 로고    scopus 로고
    • Eigenproblems for tridiagonal 2-Toeplitz matrices and quadratic polynomial mappings
    • Marcellán, F. and Petronilho, J.: Eigenproblems for tridiagonal 2-Toeplitz matrices and quadratic polynomial mappings, Linear Algebra Appl. 260 (1997), 169-208.
    • (1997) Linear Algebra Appl. , vol.260 , pp. 169-208
    • Marcellán, F.1    Petronilho, J.2
  • 36
    • 33645259640 scopus 로고    scopus 로고
    • Orthogonal polynomials and quadratic transformations
    • to appear
    • Marcellán, F. and Petronilho, J.: Orthogonal polynomials and quadratic transformations, Portugal. Math. (to appear).
    • Portugal. Math.
    • Marcellán, F.1    Petronilho, J.2
  • 37
    • 0005825078 scopus 로고
    • Differential equations for classical type orthogonal polynomials
    • Marcellán, F. and Ronveaux, A.: Differential equations for classical type orthogonal polynomials, Canad. Math. Bull 32(4) (1989), 404-411.
    • (1989) Canad. Math. Bull , vol.32 , Issue.4 , pp. 404-411
    • Marcellán, F.1    Ronveaux, A.2
  • 38
    • 0000956929 scopus 로고
    • Orthogonal Polynomials
    • Amer. Math. Soc., Providence, RI
    • Nevai, P.: Orthogonal Polynomials, Mem. Amer. Math. Soc. 213, Amer. Math. Soc., Providence, RI, 1979.
    • (1979) Mem. Amer. Math. Soc. 213
    • Nevai, P.1
  • 43
    • 0003217929 scopus 로고
    • Orthogonal Polynomials
    • Amer. Math. Soc., Providence, RI, 4th edition
    • Szegö, G.: Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ. 23, Amer. Math. Soc., Providence, RI, 1975 (4th edition).
    • (1975) Amer. Math. Soc. Colloq. Publ. 23
    • Szegö, G.1
  • 44
    • 0004255246 scopus 로고
    • Asymptotics for Orthogonal Polynomials
    • Springer-Verlag, Berlin
    • Van Assche, W.: Asymptotics for Orthogonal Polynomials, Lecture Notes in Math. 1265, Springer-Verlag, Berlin, 1987.
    • (1987) Lecture Notes in Math. 1265
    • Van Assche, W.1
  • 46
    • 38149146337 scopus 로고
    • Spectral properties of solutions of hypergeometric-type differential equations
    • Zarzo, A. and Dehesa, J. S.: Spectral properties of solutions of hypergeometric-type differential equations, J. Comput. Appl. Math. 50 (1994), 613-623.
    • (1994) J. Comput. Appl. Math. , vol.50 , pp. 613-623
    • Zarzo, A.1    Dehesa, J.S.2
  • 47
    • 0000270315 scopus 로고
    • Distribution of zeros of Gauss and Kummer hypergeometric functions: A semiclassical approach
    • Zarzo, A., Dehesa, J. S. and Yañez, R. J.: Distribution of zeros of Gauss and Kummer hypergeometric functions: A semiclassical approach, Ann. Numer. Math. 2 (1995), 457-472.
    • (1995) Ann. Numer. Math. , vol.2 , pp. 457-472
    • Zarzo, A.1    Dehesa, J.S.2    Yañez, R.J.3


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