Some inequalities involving the polygamma functions
Abstract Let ψn(x)=(−1)n−1ψ(n)(x) $\psi _{n}(x)=(-1)^{n-1}\psi ^{(n)}(x)$, where ψ(n)(x) $\psi ^{(n)}(x)$ are the polygamma functions. We determine necessary and sufficient conditions for the monotonicity and convexity of the function F(x;α,β)=ln(exp(αψ(x+β))ψn(x))−ln(n−1)!,x>max(0,−β), $$ F(x;\a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-03-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-1999-5 |