The asymptotic expansion of a generalised incomplete gamma function
نویسندگان
چکیده
منابع مشابه
A uniform asymptotic expansion for the incomplete gamma functions revisited
A new uniform asymptotic expansion for the incomplete gamma function Γ(a, z) valid for large values of z was given by the author in J. Comput. Appl. Math. 148 (2002) 323–339. This expansion contains a complementary error function of an argument measuring transition across the point z = a, with easily computable coefficients that do not involve a removable singularity in the neighbourhood of thi...
متن کاملUniform Asymptotic Expansion for the Incomplete Beta Function
In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the incomplete beta function was derived. It was not obvious from those results that the expansion is actually an asymptotic expansion. We derive a remainder estimate...
متن کاملAn asymptotic expansion for the incomplete beta function
A new asymptotic expansion is derived for the incomplete beta function I(a, b, x), which is suitable for large a, small b and x > 0.5. This expansion is of the form I(a, b, x) ∼ Q(b,−γ log x) + Γ(a+ b) Γ(a)Γ(b) x ∞ ∑
متن کاملAsymptotic and exact series representations for the incomplete Gamma function
Abstract. Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly convergent series, completely analytical, which can be used to obtain arbitrarily accurate estimates of Γ(a, x) for any value of a or x. Applications ...
متن کاملAn Asymptotic Expansion of the Double Gamma Function
The Barnes double gamma function G(z) is considered for large argument z. A new integral representation is obtained for log G(z). An asymptotic expansion in decreasing powers of z and uniformly valid for |Arg z|<? is derived from this integral. The expansion is accompanied by an error bound at any order of the approximation. Numerical experiments show that this bound is very accurate for real z...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2003
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(02)00809-9