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Then the double inequality (7.3).
(1)When, the double inequality (7.2). holds.
(i If, the double inequality (1.1).
(1)When, the double inequality (4.1).
The desired double inequality is proved.
containing the double inequality in equation (3.7).
This means that Wendel's double inequality (10) and Gautschi's first double inequality (57) are not included in each other but they all contain Gautschi's second double inequality (58).
It is shown that there holds the sharp double inequality.
This shows that the double inequality (2.16) holds.
For and, one has the following double inequality (1.13).
Finally, we give the following double inequality for π.
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