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Volumn 45, Issue 2, 2007, Pages 558-571

Computing the gamma function using contour integrals and rational approximations

Author keywords

Gamma function; Hankel contour; Numerical quadrature

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; INTEGRAL EQUATIONS; LAPLACE EQUATION;

EID: 42649135141     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/050646342     Document Type: Article
Times cited : (41)

References (25)
  • 2
    • 0035993886 scopus 로고    scopus 로고
    • Sharp constants for rational approximations of analytic functions
    • A. I. APTEKAREV, Sharp constants for rational approximations of analytic functions, Mat. Sb., 193 (2002), pp. 1-72.
    • (2002) Mat. Sb , vol.193 , pp. 1-72
    • APTEKAREV, A.I.1
  • 4
    • 0005449424 scopus 로고
    • Extended numerical computations on the "1/9" conjecture in rational approximation theory
    • Rational Approximation and Interpolation, P. R. Graves-Morris, E. B. Saff, and R. S. Varga, eds, Springer, Berlin
    • A. J. CARPENTER, A. RUTTAN, AND R. S. VARGA, Extended numerical computations on the "1/9" conjecture in rational approximation theory, in Rational Approximation and Interpolation, Lecture Notes in Math. 1105, P. R. Graves-Morris, E. B. Saff, and R. S. Varga, eds., Springer, Berlin, 1984, pp. 383-411.
    • (1984) Lecture Notes in Math , vol.1105 , pp. 383-411
    • CARPENTER, A.J.1    RUTTAN, A.2    VARGA, R.S.3
  • 6
    • 0011035926 scopus 로고
    • Leonhard Euler's integral: A historical profile of the gamma function
    • P. J. DAVIS, Leonhard Euler's integral: A historical profile of the gamma function, Amer. Math. Monthly, 66 (1959), pp. 849-869.
    • (1959) Amer. Math. Monthly , vol.66 , pp. 849-869
    • DAVIS, P.J.1
  • 8
    • 0041375523 scopus 로고    scopus 로고
    • Computing special functions by using quadrature rules
    • A. GIL, J. SEGURA, AND N. M. TEMME, Computing special functions by using quadrature rules, Numer. Algorithms, 33 (2003), pp. 265-275.
    • (2003) Numer. Algorithms , vol.33 , pp. 265-275
    • GIL, A.1    SEGURA, J.2    TEMME, N.M.3
  • 10
    • 33645378339 scopus 로고
    • Equilibrium distributions and degree of rational approximation of analytic functions
    • A. A. GONCHAR AND E. A. RAKHMANOV, Equilibrium distributions and degree of rational approximation of analytic functions, Sb. Math., 62 (1989), pp. 305-348.
    • (1989) Sb. Math , vol.62 , pp. 305-348
    • GONCHAR, A.A.1    RAKHMANOV, E.A.2
  • 11
    • 42649108181 scopus 로고
    • Die Euler'sehen Integrale bei unbeschränkter Variabilität des Arguments
    • H. HANKEL, Die Euler'sehen Integrale bei unbeschränkter Variabilität des Arguments, Z. Math. Phys., 9 (1864), pp. 1-21.
    • (1864) Z. Math. Phys , vol.9 , pp. 1-21
    • HANKEL, H.1
  • 12
    • 0007026807 scopus 로고
    • A precision approximation of the gamma function
    • C. LANCZOS, A precision approximation of the gamma function, J. Soc. Indust. Appl. Math. B, 1 (1964), pp. 86-96.
    • (1964) J. Soc. Indust. Appl. Math. B , vol.1 , pp. 86-96
    • LANCZOS, C.1
  • 13
    • 0005493050 scopus 로고
    • Asymptotics and super asymptotics of best rational approximation error norms for the exponential function (the '1/9' problem) by the Carathéodory-Fejér method
    • A. Cuyt et al, eds, Kluwer, Dordrecht
    • A. P. MAGNUS, Asymptotics and super asymptotics of best rational approximation error norms for the exponential function (the '1/9' problem) by the Carathéodory-Fejér method, in Nonlinear Methods and Rational Approximation II, A. Cuyt et al., eds., Kluwer, Dordrecht, 1994, pp. 173-185.
    • (1994) Nonlinear Methods and Rational Approximation II , pp. 173-185
    • MAGNUS, A.P.1
  • 14
    • 42649108516 scopus 로고
    • A comparison of computational methods and algorithms for the complex gamma function
    • E. W. NG, A comparison of computational methods and algorithms for the complex gamma function, ACM Trans. Math. Software, 1 (1975), pp. 56-70.
    • (1975) ACM Trans. Math. Software , vol.1 , pp. 56-70
    • NG, E.W.1
  • 17
    • 84968476556 scopus 로고
    • Calculation of the gamma function by Stirling's formula
    • R. SPIRA, Calculation of the gamma function by Stirling's formula, Math. Comp., 25 (1971), pp. 317-322.
    • (1971) Math. Comp , vol.25 , pp. 317-322
    • SPIRA, R.1
  • 18
    • 0028447840 scopus 로고
    • Computation of the gamma, digamma, and trigamma functions
    • J. L. SPOUGE, Computation of the gamma, digamma, and trigamma functions, SIAM J. Numer. Anal., 31 (1994), pp. 931-944.
    • (1994) SIAM J. Numer. Anal , vol.31 , pp. 931-944
    • SPOUGE, J.L.1
  • 19
    • 0002152334 scopus 로고
    • The accurate numerical inversion of Laplace transforms
    • A. TALBOT, The accurate numerical inversion of Laplace transforms, J. Inst. Math. Appl., 23 (1979), pp. 97-120.
    • (1979) J. Inst. Math. Appl , vol.23 , pp. 97-120
    • TALBOT, A.1
  • 22
    • 33749016203 scopus 로고    scopus 로고
    • Talbot quadratures and rational approximations
    • L. N. TREFETHEN, J. A. C. WEIDEMAN, AND T. SCHMELZER, Talbot quadratures and rational approximations, BIT, 46 (2006), pp. 653-670.
    • (2006) BIT , vol.46 , pp. 653-670
    • TREFETHEN, L.N.1    WEIDEMAN, J.A.C.2    SCHMELZER, T.3
  • 24
    • 42649121100 scopus 로고    scopus 로고
    • Parabolic and hyperbolic contours for computing the Bromwich integral
    • to appear
    • J. A. C. WEIDEMAN AND L. N. TREFETHEN, Parabolic and hyperbolic contours for computing the Bromwich integral, Math. Comp., to appear.
    • Math. Comp
    • WEIDEMAN, J.A.C.1    TREFETHEN, L.N.2
  • 25
    • 34548172888 scopus 로고    scopus 로고
    • Optimizing Talbot's contours for the inversion of the Laplace transform
    • J. A. C. WEIDEMAN, Optimizing Talbot's contours for the inversion of the Laplace transform, SIAM J. Numer. Anal., 44 (2006), pp. 2342-2362.
    • (2006) SIAM J. Numer. Anal , vol.44 , pp. 2342-2362
    • WEIDEMAN, J.A.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.