메뉴 건너뛰기




Volumn 121, Issue 1, 2000, Pages 221-246

Numerical and asymptotic aspects of parabolic cylinder functions

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS;

EID: 0034273051     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00347-2     Document Type: Article
Times cited : (49)

References (23)
  • 1
    • 85120120589 scopus 로고    scopus 로고
    • M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards Appl. Series, Vol. 55, U.S. Government Printing Office, Washington, DC, 1964 (paperback edition published by Dover, New York).
  • 2
    • 85120093135 scopus 로고    scopus 로고
    • L. Baker, C Mathematical Function Handbook, McGraw-Hill, New York, 1992. Diskette with software included.
  • 4
    • 85120103027 scopus 로고
    • H. Buchholz The Confluent Hypergeometric Function 1969 Springer Berlin
    • (1969)
    • Buchholz, H.1
  • 5
    • 85120144259 scopus 로고    scopus 로고
    • B.W. Char, K.O. Geddes, G.H. Gonnet, B.L. Leong, M.B. Monagan, S.M. Watt, Maple V, Library Reference Manual, Corr. 2nd print, Springer, New York, 1991.
  • 7
    • 85120104145 scopus 로고
    • Numerical evaluation of special functions
    • D.W. Lozier F.W.J. Olver Numerical evaluation of special functions W. Gautschi Mathematics of Computation 1943–1993: A Half-Century of Computational Mathematics PSAM 1994 AMS Providence
    • (1994)
    • Lozier, D.W.1    Olver, F.W.J.2
  • 8
    • 84956277051 scopus 로고
    • On the choice of standard solutions to Weber's equation
    • J.C.P. Miller On the choice of standard solutions to Weber's equation Proc. Cambridge Philos. Soc. 48 1952 428 435
    • (1952) Proc. Cambridge Philos. Soc. , vol.48 , pp. 428-435
    • Miller, J.C.P.1
  • 9
    • 85120108587 scopus 로고
    • J.C.P. Miller Tables of Weber Parabolic Cylinder Functions 1955 H.M. Stationary Office London
    • (1955)
    • Miller, J.C.P.1
  • 10
    • 0000949640 scopus 로고
    • Uniform asymptotic expansions for Weber parabolic cylinder functions of large order
    • F.W.J. Olver Uniform asymptotic expansions for Weber parabolic cylinder functions of large order J. Res. NBS 63B 1959 131 169
    • (1959) J. Res. NBS , vol.63B , pp. 131-169
    • Olver, F.W.J.1
  • 11
    • 85120130690 scopus 로고    scopus 로고
    • F.W.J. Olver, Asymptotics and Special Functions, Academic Press, New York, 1974 & 1997. Reprinted in 1997 by A.K. Peters.
  • 12
    • 85120102774 scopus 로고    scopus 로고
    • W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical recipes. The art of scientific computing, 2nd Edition, Cambridge University Press, Cambridge, 1992, diskettes and example books available. Editions exist in Basic (1991), C (1992), Fortran (1992), Macintosh Fortran (1988) and Pascal (1989).
  • 13
    • 0032291345 scopus 로고    scopus 로고
    • Parabolic cylinder functions of integer and half-integer orders for non-negative arguments
    • J. Segura A. Gil Parabolic cylinder functions of integer and half-integer orders for non-negative arguments Comput. Phys. Comm. 115 1998 69 86
    • (1998) Comput. Phys. Comm. , vol.115 , pp. 69-86
    • Segura, J.1    Gil, A.2
  • 14
    • 0026835779 scopus 로고
    • Parabolic cylinder functions U(n,x) for natural n and positive x
    • G. Taubmann Parabolic cylinder functions U ( n , x ) for natural n and positive x Comput. Phys. Comm. 69 1992 415 419
    • (1992) Comput. Phys. Comm. , vol.69 , pp. 415-419
    • Taubmann, G.1
  • 15
    • 0041122953 scopus 로고
    • Uniform asymptotic expansions of Laplace integrals
    • N.M. Temme Uniform asymptotic expansions of Laplace integrals Analysis 3 1983 221 249
    • (1983) Analysis , vol.3 , pp. 221-249
    • Temme, N.M.1
  • 16
    • 0039786429 scopus 로고
    • Laplace integrals: transformation to standard form and uniform asymptotic expansion
    • N.M. Temme Laplace integrals: transformation to standard form and uniform asymptotic expansion Quart. Appl. Math. XLIII 1985 103 123
    • (1985) Quart. Appl. Math. , vol.XLIII , pp. 103-123
    • Temme, N.M.1
  • 17
    • 85120107616 scopus 로고    scopus 로고
    • N.M. Temme Special Functions: An Introduction to the Classical Functions of Mathematical Physics 1996 Wiley New York
    • (1996)
    • Temme, N.M.1
  • 18
    • 21944434233 scopus 로고    scopus 로고
    • Numerical Algorithms for uniform Airy-type asymptotic expansions
    • N.M. Temme Numerical Algorithms for uniform Airy-type asymptotic expansions Numer. Algorithms 15 1997 207 225
    • (1997) Numer. Algorithms , vol.15 , pp. 207-225
    • Temme, N.M.1
  • 19
    • 85120115632 scopus 로고    scopus 로고
    • W.J. Thompson Atlas for Computing Mathematical Functions: An Illustrated Guide for Practitioners, with Programs in Fortran 90 and Mathematica. There is also an edition with programs in C 1997 Wiley New York
    • (1997)
    • Thompson, W.J.1
  • 20
    • 0006646740 scopus 로고
    • Über die Integration der partiellen Differential-gleichung: ∂2u/∂ x2+∂2u/∂ y2+k2u = 0
    • 2 u = 0 Math. Anal. 1 1869 1 36
    • (1869) Math. Anal. , vol.1 , pp. 1-36
    • Weber, H.F.1
  • 21
    • 85120094733 scopus 로고    scopus 로고
    • S. Wolfram, The Mathematica Book, 3rd Edition, Wolfram Media, Cambridge University Press, Champaign, IL, 1996.
  • 22
    • 85120109687 scopus 로고
    • R. Wong Asymptotic Approximations of Integrals 1989 Academic Press New York
    • (1989)
    • Wong, R.1
  • 23
    • 85120124395 scopus 로고    scopus 로고
    • S. Zhang, J. Jin, Computation of Special Functions, Wiley, New York, 1996. Diskette with software included.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.