About the Project
NIST

connection with incomplete gamma functions

AdvancedHelp

(0.004 seconds)

10 matching pages

1: 8.23 Statistical Applications
§8.23 Statistical Applications
2: 8.22 Mathematical Applications
§8.22(ii) Riemann Zeta Function and Incomplete Riemann Zeta Function
The function Γ ( a , z ) , with | ph a | 1 2 π and ph z = 1 2 π , has an intimate connection with the Riemann zeta function ζ ( s ) 25.2(i)) on the critical line s = 1 2 . …
3: Bibliography K
  • S. H. Khamis (1965) Tables of the Incomplete Gamma Function Ratio: The Chi-square Integral, the Poisson Distribution. Justus von Liebig Verlag, Darmstadt (German, English).
  • A. Khare and U. Sukhatme (2004) Connecting Jacobi elliptic functions with different modulus parameters. Pramana 63 (5), pp. 921–936.
  • K. S. Kölbig (1970) Complex zeros of an incomplete Riemann zeta function and of the incomplete gamma function. Math. Comp. 24 (111), pp. 679–696.
  • K. S. Kölbig (1972a) Complex zeros of two incomplete Riemann zeta functions. Math. Comp. 26 (118), pp. 551–565.
  • K. S. Kölbig (1972b) On the zeros of the incomplete gamma function. Math. Comp. 26 (119), pp. 751–755.
  • 4: Bibliography M
  • A. J. MacLeod (1989) Algorithm AS 245. A robust and reliable algorithm for the logarithm of the gamma function. Appl. Statist. 38 (2), pp. 397–402.
  • R. J. Moore (1982) Algorithm AS 187. Derivatives of the incomplete gamma integral. Appl. Statist. 31 (3), pp. 330–335.
  • T. Morita (2013) A connection formula for the q -confluent hypergeometric function. SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 050, 13.
  • C. Mortici (2011b) New sharp bounds for gamma and digamma functions. An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 57 (1), pp. 57–60.
  • C. Mortici (2013a) A continued fraction approximation of the gamma function. J. Math. Anal. Appl. 402 (2), pp. 405–410.
  • 5: Bibliography J
  • L. Jacobsen, W. B. Jones, and H. Waadeland (1986) Further results on the computation of incomplete gamma functions. In Analytic Theory of Continued Fractions, II (Pitlochry/Aviemore, 1985), W. J. Thron (Ed.), Lecture Notes in Math. 1199, pp. 67–89.
  • D. L. Jagerman (1974) Some properties of the Erlang loss function. Bell System Tech. J. 53, pp. 525–551.
  • D. K. Jefferson (1961) Algorithm 73: Incomplete elliptic integrals. Comm. ACM 4 (12), pp. 543.
  • W. B. Jones and W. J. Thron (1985) On the computation of incomplete gamma functions in the complex domain. J. Comput. Appl. Math. 12/13, pp. 401–417.
  • N. Joshi and M. D. Kruskal (1992) The Painlevé connection problem: An asymptotic approach. I. Stud. Appl. Math. 86 (4), pp. 315–376.
  • 6: Bibliography C
  • M. A. Chaudhry, N. M. Temme, and E. J. M. Veling (1996) Asymptotics and closed form of a generalized incomplete gamma function. J. Comput. Appl. Math. 67 (2), pp. 371–379.
  • M. A. Chaudhry and S. M. Zubair (1994) Generalized incomplete gamma functions with applications. J. Comput. Appl. Math. 55 (1), pp. 99–124.
  • M. A. Chaudhry and S. M. Zubair (2001) On a Class of Incomplete Gamma Functions with Applications. Chapman & Hall/CRC, Boca Raton, FL.
  • R. Cicchetti and A. Faraone (2004) Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics. IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.
  • E. D. Constantinides and R. J. Marhefka (1993) Efficient and accurate computation of the incomplete Airy functions. Radio Science 28 (4), pp. 441–457.
  • 7: Bibliography B
  • R. Barakat (1961) Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials. Math. Comp. 15 (73), pp. 7–11.
  • W. Barrett (1981) Mathieu functions of general order: Connection formulae, base functions and asymptotic formulae. I–V. Philos. Trans. Roy. Soc. London Ser. A 301, pp. 75–162.
  • M. V. Berry (1991) Infinitely many Stokes smoothings in the gamma function. Proc. Roy. Soc. London Ser. A 434, pp. 465–472.
  • W. Bühring (1994) The double confluent Heun equation: Characteristic exponent and connection formulae. Methods Appl. Anal. 1 (3), pp. 348–370.
  • R. Bulirsch (1969b) Numerical calculation of elliptic integrals and elliptic functions. III. Numer. Math. 13 (4), pp. 305–315.
  • 8: Bibliography T
  • N. M. Temme (1979b) The asymptotic expansion of the incomplete gamma functions. SIAM J. Math. Anal. 10 (4), pp. 757–766.
  • N. M. Temme (1987) On the computation of the incomplete gamma functions for large values of the parameters. In Algorithms for approximation (Shrivenham, 1985), Inst. Math. Appl. Conf. Ser. New Ser., Vol. 10, pp. 479–489.
  • N. M. Temme (1992a) Asymptotic inversion of incomplete gamma functions. Math. Comp. 58 (198), pp. 755–764.
  • N. M. Temme (1994a) A set of algorithms for the incomplete gamma functions. Probab. Engrg. Inform. Sci. 8, pp. 291–307.
  • N. M. Temme (1995a) Asymptotics of zeros of incomplete gamma functions. Ann. Numer. Math. 2 (1-4), pp. 415–423.
  • 9: Bibliography L
  • A. Laforgia (1984) Further inequalities for the gamma function. Math. Comp. 42 (166), pp. 597–600.
  • J. Lehner (1941) A partition function connected with the modulus five. Duke Math. J. 8 (4), pp. 631–655.
  • L. Levey and L. B. Felsen (1969) On incomplete Airy functions and their application to diffraction problems. Radio Sci. 4 (10), pp. 959–969.
  • J. S. Lew (1994) On the Darling-Mandelbrot probability density and the zeros of some incomplete gamma functions. Constr. Approx. 10 (1), pp. 15–30.
  • L. Lorch (1984) Inequalities for ultraspherical polynomials and the gamma function. J. Approx. Theory 40 (2), pp. 115–120.
  • 10: 10.17 Asymptotic Expansions for Large Argument
    Corresponding expansions for other ranges of ph z can be obtained by combining (10.17.3), (10.17.5), (10.17.6) with the continuation formulas (10.11.1), (10.11.3), (10.11.4) (or (10.11.7), (10.11.8)), and also the connection formula given by the second of (10.4.4). …
    §10.17(iii) Error Bounds for Real Argument and Order
    where χ ( ) = π 1 2 Γ ( 1 2 + 1 ) / Γ ( 1 2 + 1 2 ) ; see §9.7(i). … where Γ ( 1 - p , z ) is the incomplete gamma function8.2(i)). …