A Double Inequality for the Trigamma Function and Its Applications
We prove that p=1 and q=2 are the best possible parameters in the interval (0,∞) such that the double inequality ep/x+1-e-p/x/2p<ψ′x+1<eq/x+1-e-q/x/2q holds for x>0. As applications, some new approximation algorithms for the circumference ratio π and Catalan constant G=∑n=0∞-1n/(2n+1)2 are...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/702718 |