A fingers'constant is defined as to have as first decimal :
$$1.2345...$$
I ask for the most emblematic example .
For example :
$$2-\prod_{k=1}^{\infty}\left(1-\frac{1}{\left(k+1\right)e^{k}}\right)$$
Or :
$$\frac{3}{10}-\sum_{n=1}^{31}\left(-1\right)^{n}\prod_{k=1}^{100}\left(1-\frac{e^{-n}}{\left(k+1\right)^{n}e^{k^{2}n}}\right)$$
are one of these .
There is a lot of trivial examples .
As Tyma Gaidash answered my question partially I add a constraint :
Following my examples Is there some other representation for these kind of constant than the Champernowne constant series?