Complete monotonicity of a function related to the binomial probability

被引:15
作者
Alzer, Horst [1 ]
机构
[1] Morsbacher Str 10, D-51545 Waldbrol, Germany
关键词
Binomial probability; Complete monotonicity; Gamma and psi functions; Combinatorial inequalities;
D O I
10.1016/j.jmaa.2017.10.077
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let k and n be integers with 0 <= k <= n and p is an element of (0,1). We prove that the function G(a) = G (k,n,p)(a) = Gamma(an + 1)/Gamma (ak + 1)Gamma(a(n - k)p(ak) (1 - p)(a(n - k)) is completely monotonic on (0, infinity). This extends a result of Leblanc and Johnson, who showed in 2007 that the sequence {G(j)}(j=1) (infinity) is decreasing. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码:10 / 15
页数:6
相关论文
共 8 条
[1]  
Alzer H, 2002, ANN ACAD SCI FENN-M, V27, P445
[2]   Some classes of completely monotonic functions, II [J].
Alzer, Horst ;
Berg, Christian .
RAMANUJAN JOURNAL, 2006, 11 (02) :225-248
[3]  
[Anonymous], 1948, Handbook of Mathematical Functions withFormulas, Graphs, and Mathematical Tables, DOI DOI 10.1119/1.15378
[4]  
Bochner S., 1960, Harmonic analysis and the theory of probability
[5]  
Kimberling C. H., 1974, AEQUATIONES MATH, V10, P152, DOI DOI 10.1007/BF01832852
[6]  
Leblanc A., 2006, FAMILY INEQUALITIES
[7]  
LEBLANC A., 2007, J. Inequal. Pure Appl. Math., V8
[8]  
Widder D. V., 1941, The Laplace Transform