Uniform Asymptotic Expansion for the Incomplete Beta Function
نویسندگان
چکیده
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 that clearly shows that the result indeed has an asymptotic property, and we also give a recurrence relation for the coefficients.
منابع مشابه
An 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 کاملA 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 کاملOn modified asymptotic series involving confluent hypergeometric functions
A modification of standard Poincaré asymptotic expansions for functions defined by means of Laplace transforms is analyzed. This modification is based on an alternative power series expansion of the integrand, and the convergence properties are seen to be superior to those of the original asymptotic series. The resulting modified asymptotic expansion involves confluent hypergeometric functions ...
متن کاملUniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
REPORTRAPPORT Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters Abstract We consider the asymptotic behavior of the incomplete gamma functions (?a; ?z) and ?(?a; ?z) as a ! 1. Uniform expansions are needed to describe the transition area z a, in which case error functions are used as main approximants. We use integral representations of the i...
متن کاملUniform Asymptotics for the Incomplete Gamma
We consider the asymptotic behavior of the incomplete gamma functions (?a; ?z) and ?(?a; ?z) as a ! 1. Uniform expansions are needed to describe the transition area z a, in which case error functions are used as main approximants. We use integral representations of the incomplete gamma functions and derive a uniform expansion by applying techniques used for the existing uniform expansions for (...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016