The Incomplete Beta Function and its Ratio to the Complete Beta Function
نویسندگان
چکیده
منابع مشابه
On a $k$-extension of the Nielsen's $beta$-Function
Motivated by the $k$-digamma function, we introduce a $k$-extension of the Nielsen's $beta$-function, and further study some properties and inequalities of the new function.
متن کاملThe Efficient Calculation of the Incomplete Beta-Function Ratio for Half-Integer Values
(5) (i = a/(a + b), a2 = ab/[ia + b+l)ia + b)2]. Throughout this paper the following restrictions are imposed on the parameters a and b: {1} They can assume only positive half-integer values, i.e., a = k or a = k — 1/2, b = j or b = j — 1/2, where k and j are positive integers. {2} They satisfy the inequalities (6) 1/2 ^ a ^ 108, 1/2 g b ^ 60 . The purpose in this paper is to describe an effici...
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 کاملFurther Results on Generalized Incomplete Extended Beta Function
– Recently an extension of beta function is defined by introducing an extra parameter is proved to be useful earlier (Aslam Chaudhry 1997 [8] and A. R. Miller 1998 [1]). In this research note, we generalize the incomplete beta function and obtained the various integral representations and properties. Furthermore, we obtained the beta distribution for generalized beta function. Keywords––Incompl...
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: Mathematics of Computation
سال: 1968
ISSN: 0025-5718
DOI: 10.2307/2004773