Bai-Ni Guo
An inequality involving the gamma and digamma functions.
Wed, 01/26/2011 - 16:01 — SomNambulAuthors: Feng Qi, Bai-Ni Guo
Subjects: Classical Analysis and ODEs
AbstractIn the paper, we establish an inequality involving the gamma and digamma
functions and use it to prove the negativity and monotonicity of a function
involving the gamma and digamma functions.Sharp bounds for harmonic numbers.
Tue, 02/23/2010 - 16:01 — SomNambulAuthors: Feng Qi, Bai-Ni Guo
Subjects: Classical Analysis and ODEs
AbstractIn the paper, we first survey some results on inequalities for bounding
harmonic numbers or Euler-Mascheroni constant, and then we establish a new
sharp double inequality for bounding harmonic numbers as follows: For
$n\in\mathbb{N}$, the double inequality
-\frac{1}{12n^2+{2(7-12\gamma)}/{(2\gamma-1)}}\le H(n)-\ln
n-\frac1{2n}-\gamma<-\frac{1}{12n^2+6/5} is valid, with equality in the
left-hand side only when $n=1$, where the scalars
$\frac{2(7-12\gamma)}{2\gamma-1}$ and $\frac65$ are the best possible.An elegant refinement of a double inequality for the gamma function.
Tue, 01/12/2010 - 16:01 — SomNambulAuthors: Feng Qi, Bai-Ni Guo
Subjects: Classical Analysis and ODEs
AbstractWe elegantly refine a double inequality for the gamma function and improve
some known results for bounding the gamma function.Two monotonic functions involving gamma function and volume of unit ball.
Tue, 01/12/2010 - 16:01 — SomNambulAuthors: Feng Qi, Bai-Ni Guo
Subjects: Classical Analysis and ODEs
AbstractIn present paper, we prove the monotonicity of two functions involving the
gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the
unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.
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