Some Properties of a Function Originating from Geometric Probability for Pairs of Hyperplanes Intersecting with a Convex Body

Qi Feng; Mahmoud Mansour

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Some Properties of a Function Originating from Geometric Probability for Pairs of Hyperplanes Intersecting with a Convex Body

机译：一对与凸体相交的超平面的几何概率起源的函数的某些性质

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摘要

In the paper, the authors derive an integral representation, present a double inequality, supply an asymptotic formula, find an inequality, and verify complete monotonicity of a function involving the gamma function and originating from geometric probability for pairs of hyperplanes intersecting with a convex body.

机译：在本文中，作者推导了一个积分表示形式，给出了一个双重不等式，提供一个渐近公式，找到一个不等式，并验证涉及伽马函数的函数的完全单调性，并源于成对的超平面与凸体相交的几何概率。

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《Mathematical and Computational Applications》 |2016年第3期|共页
作者
Qi Feng; Mahmoud Mansour;
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中图分类数学;
关键词
gamma functioncomplete monotonicityinequalityasymptotic formulaintegral representationmonotonicity;

机译：伽玛函数完全单调性不等式渐近公式积分表示单调性;

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专利

1. On the Increasing Monotonicity of a Sequence Originating from Computation of the Probability of Intersecting between a Plane Couple and a Convex Body [J] . BAI-NI GUO, FENG QI Turkish Journal of Analysis and Number Theory . 2015,第1期

机译：由平面偶与凸体相交的概率计算得出的序列的单调性增加
2. The Probability that a Convex Body Intersects the Integer Lattice in a k-dimensional Set [J] . Roldán-Pensado E. Discrete & computational geometry . 2012,第2期

机译：凸体与k维集中的整数格相交的概率
3. Close-to-convex ??? ???? schlicht ???? ????? ?? ???? ?? (Geometric properties on the derivatives of schlicht functions including close-to-convex mappings) [J] . ??? Communications of the Korean Mathematical Society . 1989,第1期

机译：接近凸面的??? ???? schlicht ???? ?????? ?? ???? ?? （schlicht函数的导数的几何特性，包括接近凸的映射）
4. Convex Geometric Graphs with No Short Self-intersecting Paths [C] . Debra L. Boutin Southeastern International Conference on Combinatorics, Graph Theory, and Computing . 2003

机译：凸几何图，没有短的自交叉路径
5. Geometrically originated complexes and the homology of the pair (GL(,n), GM(,n)) [D] . Yagunov, Serge A. 1997

机译：几何起源的复合物和该对的同源性（GL（，n），GM（，n））
6. Weighted version of Hermite–Hadamard type inequalities for geometrically quasi-convex functions and their applications [O] . Sofian Obeidat, Muhammad Amer Latif -1

机译：几何拟凸函数的Hermite–Hadamard型不等式的加权形式及其应用
7. Lusin-Type Properties of Convex Functions and Convex Bodies [O] . Daniel Azagra, Piotr Hajłasz 2021

机译：凸函数和凸体的Lusin型特性
8. The Division of Space by Hyperplanes with Applications to Geometrical Probability [R] . Cover, T., Efron, B. 1965

机译：超平面划分空间及其在几何概率中的应用

Some Properties of a Function Originating from Geometric Probability for Pairs of Hyperplanes Intersecting with a Convex Body

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