Sharp inequalities for polygamma functions

Details Sharp inequalities for polygamma functions Sharp inequalities for polygamma functions

2009-03-11

arxiv.org/abs/0903.1984v1

Mathematics

Classical Analysis and ODEs

11 pages

Scientific paper

The main aim of this paper is to prove that the double inequality \frac{(k-1)!}{\Bigl\{x+\Bigl[\frac{(k-1)!}{|\psi^{(k)}(1)|}\Bigr]^{1/k}\Bigr\}^k} +\frac{k!}{x^{k+1}}<\bigl|\psi^{(k)}(x)\bigr|<\frac{(k-1)!}{\bigl(x+\frac12\bigr)^k}+\frac{k!}{x^{k+1}} holds for $x>0$ and $k\in\mathbb{N}$ and that the constants $\Bigl[\frac{(k-1)!}{|\psi^{(k)}(1)|}\Bigr]^{1/k}$ and $\frac12$ are the best possible. In passing, some related inequalities and (logarithmically) complete monotonicity results concerning the gamma, psi and polygamma functions are surveyed.

Affiliated with

Also associated with

No associations

Rating

Sharp inequalities for polygamma functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sharp inequalities for polygamma functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sharp inequalities for polygamma functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-124042