multivariate gamma function
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11—20 of 21 matching pages
11: Bibliography F
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Multivariate Calculation. Use of the Continuous Groups.
Springer Series in Statistics, Springer-Verlag, New York.
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Incomplete gamma functions for large values of their variables.
Adv. in Appl. Math. 34 (3), pp. 467–485.
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An asymptotic expansion of the double gamma function.
J. Approx. Theory 111 (2), pp. 298–314.
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A note on the asymptotic expansion of a ratio of gamma functions.
Proc. Edinburgh Math. Soc. (2) 15, pp. 43–45.
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Algorithm 309. Gamma function with arbitrary precision.
Comm. ACM 10 (8), pp. 511–512.
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12: 19.20 Special Cases
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►In this subsection, and also §§19.20(ii)–19.20(v), the variables of all -functions satisfy the constraints specified in §19.16(i) unless other conditions are stated.
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19.20.3
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►When the variables are real and distinct, the various cases of are called circular (hyperbolic) cases if is positive (negative), because they typically occur in conjunction with inverse circular (hyperbolic) functions.
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19.20.23
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19.20.25
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13: Bibliography P
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Tablitsy nepolnoi gamma-funktsii.
Vyčisl. Centr Akad. Nauk SSSR, Moscow (Russian).
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An asymptotic formula for the incomplete gamma function.
Ž. Vyčisl. Mat. i Mat. Fiz. 5, pp. 118–121 (Russian).
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Error bounds for the uniform asymptotic expansion of the incomplete gamma function.
J. Comput. Appl. Math. 147 (1), pp. 215–231.
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A uniform asymptotic expansion for the incomplete gamma function.
J. Comput. Appl. Math. 148 (2), pp. 323–339.
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Unbiasedness of invariant tests for MANOVA and other multivariate problems.
Ann. Statist. 8 (6), pp. 1326–1341.
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14: 18.38 Mathematical Applications
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Complex Function Theory
►The Askey–Gasper inequality … ►Eigenvalue equations involving Dunkl type operators have as eigenfunctions nonsymmetric analogues of multivariable special functions associated with root systems. … ► … ►Non-Classical Weight Functions
…15: 19.34 Mutual Inductance of Coaxial Circles
16: Bibliography M
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Algorithm AS 245. A robust and reliable algorithm for the logarithm of the gamma function.
Appl. Statist. 38 (2), pp. 397–402.
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Exact misclassification probabilities for plug-in normal quadratic discriminant functions. I. The equal-means case.
J. Multivariate Anal. 77 (1), pp. 21–53.
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Exact misclassification probabilities for plug-in normal quadratic discriminant functions. II. The heterogeneous case.
J. Multivariate Anal. 82 (2), pp. 299–330.
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A continued fraction approximation of the gamma function.
J. Math. Anal. Appl. 402 (2), pp. 405–410.
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Aspects of Multivariate Statistical Theory.
John Wiley & Sons Inc., New York.
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17: Bibliography C
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On Stieltjes’ continued fraction for the gamma function.
Math. Comp. 34 (150), pp. 547–551.
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Asymptotics and closed form of a generalized incomplete gamma function.
J. Comput. Appl. Math. 67 (2), pp. 371–379.
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Generalized incomplete gamma functions with applications.
J. Comput. Appl. Math. 55 (1), pp. 99–124.
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Multivariate Splines.
CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 54, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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Some non-central distribution problems in multivariate analysis.
Ann. Math. Statist. 34 (4), pp. 1270–1285.
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18: Bibliography B
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Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials.
Math. Comp. 15 (73), pp. 7–11.
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Infinitely many Stokes smoothings in the gamma function.
Proc. Roy. Soc. London Ser. A 434, pp. 465–472.
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On the power function of the likelihood ratio test for MANOVA.
J. Multivariate Anal. 82 (2), pp. 416–421.
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Gamma function asymptotics by an extension of the method of steepest descents.
Proc. Roy. Soc. London Ser. A 447, pp. 609–630.
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Bernoulli polynomials and asymptotic expansions of the quotient of gamma functions.
J. Comput. Appl. Math. 235 (11), pp. 3315–3331.
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19: 19.29 Reduction of General Elliptic Integrals
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►and is any permutation of the numbers , then
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►where the arguments of the
function are, in order, , , .
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can be reduced to a linear combination of basic
integrals and algebraic functions.
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►where is any permutation of the numbers , and
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►It depends primarily on multivariate recurrence relations that replace one integral by two or more.
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20: Bibliography G
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Algorithm 542: Incomplete gamma functions.
ACM Trans. Math. Software 5 (4), pp. 482–489.
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Some elementary inequalities relating to the gamma and incomplete gamma function.
J. Math. Phys. 38 (1), pp. 77–81.
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A harmonic mean inequality for the gamma function.
SIAM J. Math. Anal. 5 (2), pp. 278–281.
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A computational procedure for incomplete gamma functions.
ACM Trans. Math. Software 5 (4), pp. 466–481.
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A monotonicity property of the power function of multivariate tests.
Indag. Math. (N.S.) 11 (2), pp. 209–218.
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