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Volumn 48, Issue 1, 2006, Pages 76-96

Computing the coefficients in Laplace's method

Author keywords

Asymptotic approximation of integrals; Fa di Bruno's formula; Laplace's method; Partial Bell polynomials; Potential polynomials

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; CALCULATIONS; COMBINATORIAL MATHEMATICS; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; POLYNOMIALS;

EID: 33644601576     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036144504446175     Document Type: Article
Times cited : (26)

References (28)
  • 2
    • 0003525262 scopus 로고
    • Courcier, Paris, Reprinted in Complete Works, Vol. 7, Gauthier-Villars, Paris, 1886
    • P.-S. Laplace, Théorie Analytique des Probabilités, Vol. 1, Courcier, Paris, 1820. Reprinted in Complete Works, Vol. 7, Gauthier-Villars, Paris, 1886.
    • (1820) Théorie Analytique Des Probabilités , vol.1
    • Laplace, P.-S.1
  • 3
    • 0037106113 scopus 로고    scopus 로고
    • Laplace's method on a computer algebra system with an application to the real valued modified Bessel functions
    • B. Fabijonas, Laplace's method on a computer algebra system with an application to the real valued modified Bessel functions, J. Comput. Appl. Math., 146 (2002), pp. 323-342.
    • (2002) J. Comput. Appl. Math. , vol.146 , pp. 323-342
    • Fabijonas, B.1
  • 4
    • 33644604646 scopus 로고
    • Über die näherungsweise Berechnung von Funktionen großer Zahlen
    • O. Perron, Über die näherungsweise Berechnung von Funktionen großer Zahlen, Sitzungsber. Bayr. Akad. Wissensch. (Münch. Ber.), 1917, pp. 191-219.
    • (1917) Sitzungsber. Bayr. Akad. Wissensch. (Münch. Ber.) , pp. 191-219
    • Perron, O.1
  • 5
    • 0004284128 scopus 로고
    • Academic Press, New York, reprinted, Classics Appl. Math. 34, SIAM, Philadelphia, 2001
    • R. Wong, Asymptotic Approximations of Integrals, Academic Press, New York, 1989; reprinted, Classics Appl. Math. 34, SIAM, Philadelphia, 2001.
    • (1989) Asymptotic Approximations of Integrals
    • Wong, R.1
  • 6
    • 0039129210 scopus 로고
    • The method of Laplace
    • M. Wyman, The method of Laplace, Trans. Roy. Soc. Canada, 2 (1964), pp. 227-256.
    • (1964) Trans. Roy. Soc. Canada , vol.2 , pp. 227-256
    • Wyman, M.1
  • 11
    • 0004074709 scopus 로고
    • Academic Press, New York, reprinted, A. K. Peters, Wellesley, MA, 1997
    • F. W. J. Olver, Asymptotics and Special Functions, Academic Press, New York, 1974; reprinted, A. K. Peters, Wellesley, MA, 1997.
    • (1974) Asymptotics and Special Functions
    • Olver, F.W.J.1
  • 12
    • 0003930163 scopus 로고
    • North-Holland, Amsterdam, republished (corrected version), Dover, New York, 1981
    • N. G. De Bruijn, Asymptotic Methods in Analysis, North-Holland, Amsterdam, 1958; republished (corrected version), Dover, New York, 1981.
    • (1958) Asymptotic Methods in Analysis
    • De Bruijn, N.G.1
  • 13
    • 0004265313 scopus 로고
    • John Wiley & Sons, New York, republished, Wiley Classics Library edition, 1993
    • A. Nayfeh, Introduction to Perturbation Techniques, John Wiley & Sons, New York, 1981; republished, Wiley Classics Library edition, 1993.
    • (1981) Introduction to Perturbation Techniques
    • Nayfeh, A.1
  • 14
    • 33745878858 scopus 로고    scopus 로고
    • On the coefficients that arise from Laplace's method
    • to appear
    • J. Wojdylo, On the coefficients that arise from Laplace's method, J. Comput. Appl. Math., to appear.
    • J. Comput. Appl. Math.
    • Wojdylo, J.1
  • 16
    • 0000794806 scopus 로고
    • Exponential polynomials
    • E. T. Bell, Exponential polynomials, Ann. of Math. (2), 35 (1934), pp. 258-277.
    • (1934) Ann. of Math. (2) , vol.35 , pp. 258-277
    • Bell, E.T.1
  • 17
    • 0003862964 scopus 로고
    • John Wiley & Sons, New York, Princeton University Press, Princeton, NJ, 1980
    • J. Riordan, An Introduction to Combinatorial Analysis, John Wiley & Sons, New York, 1968; Princeton University Press, Princeton, NJ, 1980.
    • (1968) An Introduction to Combinatorial Analysis
    • Riordan, J.1
  • 18
    • 0005538651 scopus 로고
    • Dériveés des fonctions de fonctions
    • 3rd series
    • E. Cesàro, Dériveés des fonctions de fonctions, Nouvelles Annales de Mathématiques, 3rd series, 4 (1885), pp. 41-55;
    • (1885) Nouvelles Annales De Mathématiques , vol.4 , pp. 41-55
    • Cesàro, E.1
  • 19
    • 0005635131 scopus 로고
    • Edizioni Cremorese, Rome
    • Opere Scelte, Vol. 1, Edizioni Cremorese, Rome, 1964, pp. 416-429.
    • (1964) Opere Scelte , vol.1 , pp. 416-429
  • 20
    • 0036899567 scopus 로고    scopus 로고
    • Relax, but don't be too lazy
    • J. Van der Hoeven, Relax, but don't be too lazy, J. Symbolic Comput., 34 (2002), pp. 479-542.
    • (2002) J. Symbolic Comput. , vol.34 , pp. 479-542
    • van der Hoeven, J.1
  • 22
    • 0009173868 scopus 로고
    • Automatic computations with power series
    • P. Henrici, Automatic computations with power series, J. ACM, 3 (1956), pp. 10-15.
    • (1956) J. ACM , vol.3 , pp. 10-15
    • Henrici, P.1
  • 23
    • 0347984339 scopus 로고
    • Theorie des formes binaires
    • Librarie Brero, Torino
    • F. F. di Bruno, Theorie des formes binaires, Librarie Brero, Torino, 1876.
    • (1876)
    • di Bruno, F.F.1
  • 24
    • 33644586654 scopus 로고
    • Théorie générale de l'élimination
    • Lieber et Faraguet, Paris
    • F. F. di Bruno, Théorie générale de l'élimination, Lieber et Faraguet, Paris, 1859.
    • (1859)
    • di Bruno, F.F.1
  • 26
    • 0035995563 scopus 로고    scopus 로고
    • The curious history of Faà di Bruno's formula
    • W. Johnson, The curious history of Faà, di Bruno's formula, MAA Monthly, 109 (2002), pp. 217-234.
    • (2002) MAA Monthly , vol.109 , pp. 217-234
    • Johnson, W.1
  • 27
    • 84966222362 scopus 로고
    • Derivatives of composite functions
    • J. Riordan, Derivatives of composite functions, Bull. Amer. Math. Soc., 52 (1946), pp. 664-667.
    • (1946) Bull. Amer. Math. Soc. , vol.52 , pp. 664-667
    • Riordan, J.1
  • 28
    • 0039465840 scopus 로고
    • General asymptotic expansions of Laplace integrals
    • A. Erdélyi, General asymptotic expansions of Laplace integrals, Arch. Rational Mech. Anal., 7 (1961), pp. 1-20.
    • (1961) Arch. Rational Mech. Anal. , vol.7 , pp. 1-20
    • Erdélyi, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.