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Volumn 16, Issue , 2007, Pages 379-478

Numerical aspects of special functions

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EID: 35348895185     PISSN: 09624929     EISSN: 14740508     Source Type: Journal    
DOI: 10.1017/S0962492906330012     Document Type: Article
Times cited : (15)

References (82)
  • 1
    • 0003283055 scopus 로고
    • Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
    • of series, US Printing Office
    • M. Abramowitz and I. A. Stegun (1964), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Vol. 55 of National Bureau of Standards Applied Mathematics series, US Printing Office.
    • (1964) National Bureau of Standards Applied Mathematics , vol.55
    • Abramowitz, M.1    Stegun, I.A.2
  • 5
    • 84966220372 scopus 로고
    • Rational Chebyshev approximations for the inverse of the error function
    • J. M. Blair, C. A. Edwards and J. H. Johnson (1976), 'Rational Chebyshev approximations for the inverse of the error function', Math. Comp. 30, 7-68.
    • (1976) Math. Comp , vol.30 , pp. 7-68
    • Blair, J.M.1    Edwards, C.A.2    Johnson, J.H.3
  • 6
    • 0004639723 scopus 로고
    • Comparison of some methods for evaluating infinite range oscillatory integrals
    • M. Blakemore, G. A. Evans and J. Hyslop (1976), 'Comparison of some methods for evaluating infinite range oscillatory integrals', J. Comput. Phys. 22, 352-376.
    • (1976) J. Comput. Phys , vol.22 , pp. 352-376
    • Blakemore, M.1    Evans, G.A.2    Hyslop, J.3
  • 8
    • 0040617191 scopus 로고
    • An analytic continuation of the hypergeometric series
    • W. Bühring (1987), 'An analytic continuation of the hypergeometric series', SIAM J. Math. Anal. 18, 884-889.
    • (1987) SIAM J. Math. Anal , vol.18 , pp. 884-889
    • Bühring, W.1
  • 9
    • 4043156369 scopus 로고
    • A method for numerical calculation of Fourier integrals
    • W. W. Clendenin (1966), 'A method for numerical calculation of Fourier integrals', Numer. Math. 8, 422-436.
    • (1966) Numer. Math , vol.8 , pp. 422-436
    • Clendenin, W.W.1
  • 10
    • 84975966072 scopus 로고
    • The numerical solution of linear differential equations in Chebyshev series
    • C. W. Clenshaw (1957), 'The numerical solution of linear differential equations in Chebyshev series', Proc. Cambridge Philos. Soc. 53, 134-149.
    • (1957) Proc. Cambridge Philos. Soc , vol.53 , pp. 134-149
    • Clenshaw, C.W.1
  • 12
    • 35348893315 scopus 로고    scopus 로고
    • Transitory minimal solutions of hypergeometric recursions and pseudoconvergence of associated continued fractions
    • A. Deaño and J. Segura (2007), 'Transitory minimal solutions of hypergeometric recursions and pseudoconvergence of associated continued fractions', Math. Comp. 76, 879-901.
    • (2007) Math. Comp , vol.76 , pp. 879-901
    • Deaño, A.1    Segura, J.2
  • 13
    • 0010540006 scopus 로고
    • Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type
    • W. Eckhaus and E. M. de Jager (1966), 'Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type', Arch. Rational Mech. Anal. 23, 26-86.
    • (1966) Arch. Rational Mech. Anal , vol.23 , pp. 26-86
    • Eckhaus, W.1    de Jager, E.M.2
  • 14
    • 0346130297 scopus 로고
    • The trapezoidal rule for analytic functions of rapid decrease
    • N. Eggert and J. Lund (1989), 'The trapezoidal rule for analytic functions of rapid decrease', J. Comput. Appl. Math. 27, 389-406.
    • (1989) J. Comput. Appl. Math , vol.27 , pp. 389-406
    • Eggert, N.1    Lund, J.2
  • 15
    • 0003504382 scopus 로고    scopus 로고
    • An Introduction to Difference Equations
    • 3rd edn, Springer, New York
    • S. Elaydi (2005), An Introduction to Difference Equations, Undergraduate Texts in Mathematics, 3rd edn, Springer, New York.
    • (2005) Undergraduate Texts in Mathematics
    • Elaydi, S.1
  • 16
    • 0002374955 scopus 로고    scopus 로고
    • Sigmoidal transformations and the trapezoidal rule
    • electronic
    • D. Elliott (1998/99), 'Sigmoidal transformations and the trapezoidal rule', J. Austral. Math. Soc. Ser. B 40, E77-E137 (electronic).
    • (1998) J. Austral. Math. Soc. Ser. B , vol.40
    • Elliott, D.1
  • 17
    • 14844297763 scopus 로고    scopus 로고
    • Incomplete gamma functions for large values of their variables
    • C. Ferreira, J. L. López and E. Pérez Sinusía (2005), 'Incomplete gamma functions for large values of their variables', Adv. in Appl. Math. 34, 467-485.
    • (2005) Adv. in Appl. Math , vol.34 , pp. 467-485
    • Ferreira, C.1    López, J.L.2    Pérez Sinusía, E.3
  • 18
    • 0005054331 scopus 로고
    • On a quadrature formula for trigonometric integrals
    • L. N. G. Filon (1928), 'On a quadrature formula for trigonometric integrals', Proc. Roy. Soc. Edinburgh 49, 38-47.
    • (1928) Proc. Roy. Soc. Edinburgh , vol.49 , pp. 38-47
    • Filon, L.N.G.1
  • 19
    • 0004578096 scopus 로고    scopus 로고
    • Computing the hypergeometric function
    • R. C. Forrey (1997), 'Computing the hypergeometric function', J. Comput. Phys. 137, 79-100.
    • (1997) J. Comput. Phys , vol.137 , pp. 79-100
    • Forrey, R.C.1
  • 20
    • 0002334558 scopus 로고
    • Computational aspects of three-term recurrence relations
    • W. Gautschi (1967), 'Computational aspects of three-term recurrence relations', SIAM Rev. 9, 24-82.
    • (1967) SIAM Rev , vol.9 , pp. 24-82
    • Gautschi, W.1
  • 21
    • 84966261673 scopus 로고
    • Anomalous convergence of a continued fraction for ratios of Kummer functions
    • W. Gautschi (1977), 'Anomalous convergence of a continued fraction for ratios of Kummer functions', Math. Comp. 31, 994-999.
    • (1977) Math. Comp , vol.31 , pp. 994-999
    • Gautschi, W.1
  • 22
    • 14844339312 scopus 로고    scopus 로고
    • Orthogonal Polynomials: Computation and Approximation
    • Oxford University Press, New York
    • W. Gautschi (2004), Orthogonal Polynomials: Computation and Approximation, Numerical Mathematics and Scientific Computation series, Oxford University Press, New York.
    • (2004) Numerical Mathematics and Scientific Computation series
    • Gautschi, W.1
  • 23
    • 0031246127 scopus 로고    scopus 로고
    • Evaluation of Legendre functions of argument greater than one
    • A. Gil and J. Segura (1997), 'Evaluation of Legendre functions of argument greater than one', Comput. Phys. Comm. 105, 273-283.
    • (1997) Comput. Phys. Comm , vol.105 , pp. 273-283
    • Gil, A.1    Segura, J.2
  • 24
    • 0034650146 scopus 로고    scopus 로고
    • Evaluation of toroidal harmonics
    • A. Gil and J. Segura (2000), 'Evaluation of toroidal harmonics', Comput. Phys. Comm. 124, 104-122.
    • (2000) Comput. Phys. Comm , vol.124 , pp. 104-122
    • Gil, A.1    Segura, J.2
  • 26
    • 40249085363 scopus 로고    scopus 로고
    • Numerically satisfactory solutions of hypergeometric recursions
    • to appear
    • A. Gil, J. Segura and N. M. Temme (2007a), 'Numerically satisfactory solutions of hypergeometric recursions', Math. Comp., to appear.
    • (2007) Math. Comp
    • Gil, A.1    Segura, J.2    Temme, N.M.3
  • 27
    • 43049104350 scopus 로고    scopus 로고
    • Numerical Methods for Special Functions, SIAM, Philadelphia, PA
    • To appear
    • A. Gil, J. Segura and N. M. Temme (2007b), Numerical Methods for Special Functions, SIAM, Philadelphia, PA. To appear.
    • (2007)
    • Gil, A.1    Segura, J.2    Temme, N.M.3
  • 30
    • 0040647284 scopus 로고
    • The tanh rule for numerical integration
    • S. Haber (1977), 'The tanh rule for numerical integration', SIAM J. Numer. Anal. 14, 668-685.
    • (1977) SIAM J. Numer. Anal , vol.14 , pp. 668-685
    • Haber, S.1
  • 31
    • 4043159167 scopus 로고    scopus 로고
    • On the numerical quadrature of highly-oscillating integrals I: Fourier transforms
    • A. Iserles (2004), 'On the numerical quadrature of highly-oscillating integrals I: Fourier transforms', IMA J. Numer. Anal. 24, 365-391.
    • (2004) IMA J. Numer. Anal , vol.24 , pp. 365-391
    • Iserles, A.1
  • 32
    • 11444264626 scopus 로고    scopus 로고
    • On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators
    • A. Iserles (2005), 'On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators', IMA J. Numer. Anal. 25, 25-44.
    • (2005) IMA J. Numer. Anal , vol.25 , pp. 25-44
    • Iserles, A.1
  • 33
  • 34
    • 0040984922 scopus 로고
    • On the general Hermite cardinal interpolation
    • R. Kreß (1972), 'On the general Hermite cardinal interpolation', Math. Comp. 26, 925-933.
    • (1972) Math. Comp , vol.26 , pp. 925-933
    • Kreß, R.1
  • 35
    • 84983962268 scopus 로고
    • Anwendung der Rechteckregel auf die reelle Hilbertransformation mit unendlichem Intervall
    • R. Kress and E. Martensen (1970), 'Anwendung der Rechteckregel auf die reelle Hilbertransformation mit unendlichem Intervall', Z. Angew. Math. Mech. 50, T61-T64.
    • (1970) Z. Angew. Math. Mech , vol.50
    • Kress, R.1    Martensen, E.2
  • 36
    • 84981860586 scopus 로고
    • Error estimates for Luke's approximation formulas for Bessel and Hankel functions
    • H. Krumhaar (1965), 'Error estimates for Luke's approximation formulas for Bessel and Hankel functions', Z. Angew. Math. Mech. 45, 245-255.
    • (1965) Z. Angew. Math. Mech , vol.45 , pp. 245-255
    • Krumhaar, H.1
  • 37
    • 84971194573 scopus 로고
    • Note on a method for computing infinite integrals of oscillatory functions
    • I. M. Longman (1956), 'Note on a method for computing infinite integrals of oscillatory functions', Proc. Cambridge Philos. Soc. 52, 764-768.
    • (1956) Proc. Cambridge Philos. Soc , vol.52 , pp. 764-768
    • Longman, I.M.1
  • 38
    • 35348833043 scopus 로고    scopus 로고
    • D. W. Lozier and F. W. J. Olver (1994), Numerical evaluation of special functions, in Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics (Vancouver, BC, 1993), 48 of Proc. Sympos. Appl. Math., AMS, Providence, RI, pp. 79-125. Updates are available at http://math.nist.gov/mcsd/Reports/2001/nesf/.
    • D. W. Lozier and F. W. J. Olver (1994), Numerical evaluation of special functions, in Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics (Vancouver, BC, 1993), Vol. 48 of Proc. Sympos. Appl. Math., AMS, Providence, RI, pp. 79-125. Updates are available at http://math.nist.gov/mcsd/Reports/2001/nesf/.
  • 39
    • 0000785381 scopus 로고
    • Evaluating infinite integrals involving Bessel functions of arbitrary order
    • S. K. Lucas and H. A. Stone (1995), 'Evaluating infinite integrals involving Bessel functions of arbitrary order', J. Comput. Appl. Math. 64, 217-231.
    • (1995) J. Comput. Appl. Math , vol.64 , pp. 217-231
    • Lucas, S.K.1    Stone, H.A.2
  • 40
    • 0012577114 scopus 로고
    • The Special Functions and their Approximations I
    • of, Academic Press, New York
    • Y. L. Luke (1969a), The Special Functions and their Approximations I, Vol. 53 of Mathematics in Science and Engineering, Academic Press, New York.
    • (1969) Mathematics in Science and Engineering , vol.53
    • Luke, Y.L.1
  • 41
    • 35348831837 scopus 로고    scopus 로고
    • Y. L. Luke (19696), The Special Functions and their Approximations II, 53 of Mathematics in Science and Engineering, Academic Press, New York.
    • Y. L. Luke (19696), The Special Functions and their Approximations II, Vol. 53 of Mathematics in Science and Engineering, Academic Press, New York.
  • 43
    • 84941524798 scopus 로고
    • A statistical theory of target detection by pulsed radar
    • J. I. Marcum (1960), 'A statistical theory of target detection by pulsed radar', Trans. IRE IT-6, 59-267.
    • (1960) Trans. IRE , vol.IT-6 , pp. 59-267
    • Marcum, J.I.1
  • 44
    • 84968466438 scopus 로고
    • Uniform computation of the error function and other related functions
    • F. Matta and A. Reichel (1971), 'Uniform computation of the error function and other related functions', Math. Comp. 25, 339-344.
    • (1971) Math. Comp , vol.25 , pp. 339-344
    • Matta, F.1    Reichel, A.2
  • 45
    • 0039498934 scopus 로고
    • On the superiority of the trapezoidal rule for the integration of periodic analytic functions
    • M. Mori (1974), 'On the superiority of the trapezoidal rule for the integration of periodic analytic functions', Mem. Numer. Math. 1, 11-19.
    • (1974) Mem. Numer. Math , vol.1 , pp. 11-19
    • Mori, M.1
  • 47
    • 0025448483 scopus 로고
    • Algorithm 682: Talbot's method for the Laplace inversion problem
    • A. Murli and M. Rizzardi (1990), 'Algorithm 682: Talbot's method for the Laplace inversion problem', ACM Trans. Math. Software 16, 158-168.
    • (1990) ACM Trans. Math. Software , vol.16 , pp. 158-168
    • Murli, A.1    Rizzardi, M.2
  • 48
    • 0039022112 scopus 로고
    • Numerical solution of second-order linear difference equations
    • F. W. J. Olver (1967), 'Numerical solution of second-order linear difference equations', J. Res. Nat. Bur. Standards Sect. B 71B, 111-129.
    • (1967) J. Res. Nat. Bur. Standards Sect. B , vol.71 B , pp. 111-129
    • Olver, F.W.J.1
  • 49
    • 35348815069 scopus 로고    scopus 로고
    • F. W. J. Olver (1997), Asymptotics and Special Functions, AKP Classics, A. K. Peters, Wellesley, MA. Reprint of the 1974 original (Academic Press, New York).
    • F. W. J. Olver (1997), Asymptotics and Special Functions, AKP Classics, A. K. Peters, Wellesley, MA. Reprint of the 1974 original (Academic Press, New York).
  • 50
    • 0037113844 scopus 로고    scopus 로고
    • A uniform asymptotic expansion for the incomplete gamma function
    • R. B. Paris (2002), 'A uniform asymptotic expansion for the incomplete gamma function', J. Comput. Appl. Math. 148, 323-339.
    • (2002) J. Comput. Appl. Math , vol.148 , pp. 323-339
    • Paris, R.B.1
  • 51
    • 34250381856 scopus 로고
    • On high precision methods for the evaluation of Fourier integrals with finite and infinite limits
    • T. N. L. Patterson (1976/77), 'On high precision methods for the evaluation of Fourier integrals with finite and infinite limits', Numer. Math. 27, 41-52.
    • (1976) Numer. Math , vol.27 , pp. 41-52
    • Patterson, T.N.L.1
  • 53
    • 0015630104 scopus 로고
    • Efficient evaluation of integrals of analytic functions by the trapezoidal rule
    • S. O. Rice (1973), 'Efficient evaluation of integrals of analytic functions by the trapezoidal rule', Bell System Tech. J. 52, 707-722.
    • (1973) Bell System Tech. J , vol.52 , pp. 707-722
    • Rice, S.O.1
  • 54
    • 0000799469 scopus 로고
    • A modification of Talbot's method for the simultaneous approximation of several values of the inverse Laplace transform
    • M. Rizzardi (1995), 'A modification of Talbot's method for the simultaneous approximation of several values of the inverse Laplace transform', ACM Trans. Math. Software 21, 347-371.
    • (1995) ACM Trans. Math. Software , vol.21 , pp. 347-371
    • Rizzardi, M.1
  • 55
    • 84977687924 scopus 로고
    • Computation of the noncentral chi-square distribution
    • G. Robertson (1969), 'Computation of the noncentral chi-square distribution', Bell. System Tech. J. 48, 201-207.
    • (1969) Bell. System Tech. J , vol.48 , pp. 201-207
    • Robertson, G.1
  • 56
    • 0016900424 scopus 로고
    • An efficient iterative method for numerical evaluation of integrals over a semi-infinite range
    • W. Squire (1976a), 'An efficient iterative method for numerical evaluation of integrals over a semi-infinite range', Internat. J. Numer. Methods Engrg. 10, 478-484.
    • (1976) Internat. J. Numer. Methods Engrg , vol.10 , pp. 478-484
    • Squire, W.1
  • 57
    • 84985407655 scopus 로고    scopus 로고
    • (19766), 'A quadrature method for finite intervals
    • W. Squire (19766), 'A quadrature method for finite intervals', Internat. J. Numer. Methods Engrg. 11, 708-712.
    • Internat. J. Numer. Methods Engrg , vol.11 , pp. 708-712
    • Squire, W.1
  • 58
    • 84968494987 scopus 로고
    • On the calculation of the inverse of the error function
    • A. Strecok (1968), 'On the calculation of the inverse of the error function', Math. Comp. 22, 144-158.
    • (1968) Math. Comp , vol.22 , pp. 144-158
    • Strecok, A.1
  • 59
    • 0039614324 scopus 로고
    • Error estimation in the numerical integration of analytic functions
    • H. Takahasi and M. Mori (1970), 'Error estimation in the numerical integration of analytic functions', Rep. Comput. Centre Univ. Tokyo 3, 41-108.
    • (1970) Rep. Comput. Centre Univ. Tokyo , vol.3 , pp. 41-108
    • Takahasi, H.1    Mori, M.2
  • 60
    • 84951414107 scopus 로고
    • Estimation of errors in the numerical quadrature of analytic functions
    • H. Takahasi and M. Mori (1971), 'Estimation of errors in the numerical quadrature of analytic functions.', Applicable Anal. 1, 201-229.
    • (1971) Applicable Anal , vol.1 , pp. 201-229
    • Takahasi, H.1    Mori, M.2
  • 61
    • 0010118546 scopus 로고
    • Quadrature formulas obtained by variable transformation
    • H. Takahasi and M. Mori (1973/74), 'Quadrature formulas obtained by variable transformation', Numer. Math. 21, 206-219.
    • (1973) Numer. Math , vol.21 , pp. 206-219
    • Takahasi, H.1    Mori, M.2
  • 62
    • 0002152334 scopus 로고
    • The accurate numerical inversion of Laplace transforms
    • A. Talbot (1979), 'The accurate numerical inversion of Laplace transforms', J. Inst. Math. Appl. 23, 97-120.
    • (1979) J. Inst. Math. Appl , vol.23 , pp. 97-120
    • Talbot, A.1
  • 63
    • 0001493093 scopus 로고
    • The uniform asymptotic expansion of a class of integrals related to cumulative distribution functions
    • N. M. Temme (1982), 'The uniform asymptotic expansion of a class of integrals related to cumulative distribution functions', SIAM J. Math. Anal. 13, 239-253.
    • (1982) SIAM J. Math. Anal , vol.13 , pp. 239-253
    • Temme, N.M.1
  • 64
    • 84968501834 scopus 로고
    • Asymptotic inversion of incomplete gamma functions
    • N. M. Temme (1992a), 'Asymptotic inversion of incomplete gamma functions', Math. Comp. 58, 755-764.
    • (1992) Math. Comp , vol.58 , pp. 755-764
    • Temme, N.M.1
  • 65
    • 38249008985 scopus 로고    scopus 로고
    • (19926), 'Asymptotic inversion of the incomplete beta function
    • N. M. Temme (19926), 'Asymptotic inversion of the incomplete beta function', J. Comput. Appl. Math. 41, 145-157.
    • J. Comput. Appl. Math , vol.41 , pp. 145-157
    • Temme, N.M.1
  • 66
    • 38249004117 scopus 로고
    • Asymptotic and numerical aspects of the noncentral chisquare distribution
    • N. M. Temme (1993), 'Asymptotic and numerical aspects of the noncentral chisquare distribution', Comput. Math. Appl. 25, 55-63.
    • (1993) Comput. Math. Appl , vol.25 , pp. 55-63
    • Temme, N.M.1
  • 68
    • 21944434233 scopus 로고    scopus 로고
    • Numerical algorithms for uniform Airy-type asymptotic expansions
    • N. M. Temme (1997), 'Numerical algorithms for uniform Airy-type asymptotic expansions', Numer. Algorithms 15, 207-225.
    • (1997) Numer. Algorithms , vol.15 , pp. 207-225
    • Temme, N.M.1
  • 69
    • 34547127425 scopus 로고    scopus 로고
    • Analytical methods for an elliptic singular perturbation problem in a circle
    • to appear
    • N. M. Temme (2007), 'Analytical methods for an elliptic singular perturbation problem in a circle', J. Comput. Appl. Math., to appear.
    • (2007) J. Comput. Appl. Math
    • Temme, N.M.1
  • 71
    • 35348813251 scopus 로고    scopus 로고
    • Talbot quadrature and rational approximations
    • Technical report, Oxford University Computing Laboratory, Numerical Analysis Group
    • L. N. Trefethen, J. Weideman and T. Schmelzer (2005), Talbot quadrature and rational approximations. Technical report, Oxford University Computing Laboratory, Numerical Analysis Group.
    • (2005)
    • Trefethen, L.N.1    Weideman, J.2    Schmelzer, T.3
  • 72
    • 0036576559 scopus 로고    scopus 로고
    • Symbolic evaluation of coefficients in Airytype asymptotic expansions
    • R. Vidunas and N. M. Temme (2002), 'Symbolic evaluation of coefficients in Airytype asymptotic expansions', J. Math. Anal. Appl. 269, 317-331.
    • (2002) J. Math. Anal. Appl , vol.269 , pp. 317-331
    • Vidunas, R.1    Temme, N.M.2
  • 73
    • 0004108644 scopus 로고
    • World Scientific, Teaneck, NJ. Translated from the Chinese by Guo and X. J. Xia
    • Z. X. Wang and D. R. Guo (1989), Special Functions, World Scientific, Teaneck, NJ. Translated from the Chinese by Guo and X. J. Xia.
    • (1989) Special Functions
    • Wang, Z.X.1    Guo, D.R.2
  • 74
    • 0036001757 scopus 로고    scopus 로고
    • Numerical integration of periodic functions: A few examples
    • J. A. C. Weideman (2002), 'Numerical integration of periodic functions: A few examples', Amer. Math. Monthly 109, 21-36.
    • (2002) Amer. Math. Monthly , vol.109 , pp. 21-36
    • Weideman, J.A.C.1
  • 75
    • 35348887298 scopus 로고    scopus 로고
    • Optimizing Talbot's contours for the inversion of the Laplace transform
    • Technical Report NA 05/05, Oxford University Computing Laboratory
    • J. A. C. Weideman (2005), Optimizing Talbot's contours for the inversion of the Laplace transform. Technical Report NA 05/05, Oxford University Computing Laboratory.
    • (2005)
    • Weideman, J.A.C.1
  • 76
    • 0343863901 scopus 로고
    • Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series
    • E. J. Weniger (1989), 'Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series', Computer Physics Reports 10, 189-371.
    • (1989) Computer Physics Reports , vol.10 , pp. 189-371
    • Weniger, E.J.1
  • 77
    • 0003991840 scopus 로고
    • Computation with Recurrence Relations
    • Pitman Advanced Publishing Program, Boston, MA
    • J. Wimp (1984), Computation with Recurrence Relations, Applicable Mathematics series, Pitman (Advanced Publishing Program), Boston, MA.
    • (1984) Applicable Mathematics series
    • Wimp, J.1
  • 78
    • 0042399511 scopus 로고
    • Quadrature formulas for oscillatory integral transforms
    • R. Wong (1982), 'Quadrature formulas for oscillatory integral transforms', Numer. Math. 39, 351-360.
    • (1982) Numer. Math , vol.39 , pp. 351-360
    • Wong, R.1
  • 79
    • 35348912030 scopus 로고    scopus 로고
    • R. Wong (2001), Asymptotic Approximations of Integrals, 34 of Classics in Applied Mathematics, SIAM, Philadelphia, PA. Corrected reprint of the 1989 original.
    • R. Wong (2001), Asymptotic Approximations of Integrals, Vol. 34 of Classics in Applied Mathematics, SIAM, Philadelphia, PA. Corrected reprint of the 1989 original.
  • 80
    • 0012993065 scopus 로고
    • Asymptotic expansions for second-order linear difference equations
    • R. Wong and H. Li (1992a), 'Asymptotic expansions for second-order linear difference equations', J. Comput. Appl. Math. 41, 65-94.
    • (1992) J. Comput. Appl. Math , vol.41 , pp. 65-94
    • Wong, R.1    Li, H.2
  • 81
    • 0040803095 scopus 로고    scopus 로고
    • (19926), 'Asymptotic expansions for second-order linear difference equations II
    • R. Wong and H. Li (19926), 'Asymptotic expansions for second-order linear difference equations II, Stud. Appl. Math. 87, 289-324.
    • Stud. Appl. Math , vol.87 , pp. 289-324
    • Wong, R.1    Li, H.2


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