A Double Inequality for the Trigamma Function and Its Applications

Table 1

𝑛	|6𝑄𝑛−𝜋|	|6𝑙𝑛−𝜋|	|6𝐿𝑛−𝜋|
1	0.6921	4.3127×10^−3	7.663×10^−4
2	0.40298	3.7549×10^−4	2.8250×10^−5
5	0.1782	7.7596×10^−6	1.3276×10^−7
10	9.2231×10^−2	3.1013×10^−7	1.4875×10^−9
50	1.8966×10^−2	1.2112×10^−10	2.5320×10^−14
100	9.5161×10^−3	3.8807×10^−12	2.0489×10^−16
200	4.7663×10^−3	1.2280×10^−13	1.6291×10^−18
500	1.9085×10^−3	1.2669×10^−15	2.6973×10^−21