Monotonicity of a mean related to polygamma functions with an application
Abstract Let ψ n = ( − 1 ) n − 1 $\psi_{n}= ( -1 ) ^{n-1}$ ψ ( n ) $\psi^{ ( n ) }$ ( n = 0 , 1 , 2 , … $n=0,1,2,\ldots $ ), where ψ ( n ) $\psi^{ ( n ) }$ denotes the psi and polygamma functions. We prove that for n ≥ 0 $n\geq0$ and two different real numbers a and b, the function x ↦ ψ n − 1 ( ∫ a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016-09-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1155-4 |