A Note on the Hypergeometric Mean Value
نویسندگان
چکیده
in terms of power means and other related means have precipitated the search for similar bounds for the more general 2F1(α, β; γ; r). In an early paper, B. C. Carlson considered the approximation of the hypergeometric mean values ( 2F1(−a, b; b + c; r)) in terms of means of order t, given by Mt(s, r) := {(1 − s) + s(1 − r)t}1/t. In this note, a refinement of one such approximation is established by first proving a general positivity result involving 3F2.
منابع مشابه
ON AN EXTENSION OF A QUADRATIC TRANSFORMATION FORMULA DUE TO GAUSS
The aim of this research note is to prove the following new transformation formula begin{equation*} (1-x)^{-2a},_{3}F_{2}left[begin{array}{ccccc} a, & a+frac{1}{2}, & d+1 & & \ & & & ; & -frac{4x}{(1-x)^{2}} \ & c+1, & d & & end{array}right] \ =,_{4}F_{3}left[begin{array}{cccccc} 2a, & 2a-c, & a-A+1, & a+A+1 & & \ & & & & ; & -x \ & c+1, & a-A, & a+A & & end{array} right], end{equation*} wher...
متن کاملOn Inequalities for Hypergeometric Analogues of the Arithmetic-geometric Mean
In this note, we present sharp inequalities relating hypergeometric analogues of the arithmetic-geometric mean discussed in [5] and the power mean. The main result generalizes the corresponding sharp inequality for the arithmetic-geometric mean established in [10].
متن کاملDegenerate Gauss hypergeometric functions
Throughout the paper, we denote this equation by E(a, b, c). Since Kummer we know that in general there are 24 hypergeometric series which express solutions of E(a, b, c). The subject of this paper is Gauss hypergeometric functions when some or all of the numbers a, b, c, c − a, c − b, a − b, c − a − b are integers. We refer to these functions and to corresponding hypergeometric equations as de...
متن کاملAcceptance sampling for attributes via hypothesis testing and the hypergeometric distribution
This paper questions some aspects of attribute acceptance sampling in light of the original concepts of hypothesis testing from Neyman and Pearson (NP). Attribute acceptance sampling in industry, as developed by Dodge and Romig (DR), generally follows the international standards of ISO 2859, and similarly the Brazilian standards NBR 5425 to NBR 5427 and the United States Standards ANSI/ASQC Z1....
متن کاملExperimental and Numerical Flow Investigation of Intake Manifold and Multi Criteria Decision Making on 3-cylinder SI Engine using Technique for Order of Preference by Similarity to Ideal Solution (RESEARCH NOTE)
In this paper, technique for order of preference by similarity to ideal solution(TOPSIS) method is used to find the best compromising design of intake manifold for a 3-cylinder engine considering mean value of torque, torque at 3500 rpm, mean value of brake mean specific consumption (BSFC) and BSFC at 3500 rpmas four objective functions. To calculate the objective functions, engine simulation i...
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 2001