Inequalities for the beta function of n variables
نویسندگان
چکیده
منابع مشابه
Inequalities for the Beta function
Let g(x) := (e/x)xΓ(x+ 1) and F(x,y) := g(x)g(y)/g(x + y) . Let D x,y be the k th differential in Taylor’s expansion of logF(x,y) . We prove that when (x,y) ∈ R+ one has (−1)k−1D x,y (X ,Y ) > 0 for every X ,Y ∈ R+ , and that when k is even the conclusion holds for every X ,Y ∈ R with (X ,Y ) = (0,0) . This implies that Taylor’s polynomials for logF provide upper and lower bounds for logF accor...
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ژورنال
عنوان ژورنال: The ANZIAM Journal
سال: 2003
ISSN: 1446-1811,1446-8735
DOI: 10.1017/s1446181100012979