Du Bois Reymond constants

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The Du Bois Reymond constant $C_{n}$ for a given number $n$ is $2\sum _{i=1}^{\infty }({x_{i}}^{2}+1)^{\frac {-n}{2}}$ with $x_{i}$ being the $i$th root of $i=\tan i$.

In the following table, the decimal expansions are given truncated to twelve decimal places.

$n$	Decimal expansion		Continued fraction
2	0.194528049465	A062546	0, 5, 7, 9, 11, 13, 15, 17, ...	A062545
3	0.028251764160	A224196
4	0.005240704677	A207528	0, 190, 1, 4, 2, 1, 1, 1, 6, ...	A138730
5	0.001056102107	A243108
6	0.000220674708	A245333	0, 4531, 1, 1, 3, 1, 8, 3, 2, ...	A138731
7
8			0, 99232, 2, 6, 1, 3, 4, 2, ...	A138732
				(See also A138733).