On Alzer and Qiu's Conjecture for Complete Elliptic Integral and Inverse Hyperbolic Tangent Function
We prove that the double inequality (π/2)(arthr/r)3/4+α*r<K(r)<(π/2)(arthr/r)3/4+β*r holds for all r∈(0,1) with the best possible constants α*=0 and β*=1/4, which answer to an open problem proposed by Alzer and Qiu. Here, K(r) is the complete elliptic integrals of the first kind, and arth is t...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/697547 |
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