INCOMPLETE q-GAMMA FUNCTION AND TRICOMI EXPANSION
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 کاملOn the Incomplete Gamma Function and the Neutrix Convolution
The incomplete Gamma function γ(α, x) and its associated functions γ(α, x+) and γ(α, x−) are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions x and x − are then found.
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 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 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 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 Nonlinear Mathematical Physics
سال: 2021
ISSN: 1776-0852
DOI: 10.1142/s1402925109000133