The monotonicity and convexity of a function involving psi function with applications
Abstract In this paper, we prove that the function x ↦ exp ( ψ ( x + 1 2 ) − 1 24 1 x 2 + 7 / 40 ) − x $$ x\mapsto\exp \biggl( \psi \biggl( x+\frac{1}{2} \biggr) -\frac {1}{24} \frac{1}{x^{2}+7/40} \biggr) -x $$ is decreasing from ( − 1 / 2 , ∞ ) $( -1/2,\infty ) $ onto ( 0 , 1 / 2 ) $( 0,1/2 ) $ an...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1084-2 |