When I started learning Riemann zeta function, I was fascinated that $\zeta(2n)$ can be expressed with finite integers and $\pi$ while $\pi$ has no obvious relation with the sum-$\zeta(2n)$ but no "magical" constant can be used to express $\zeta(2n+1)$ like that. Afterwards, I learned that Euler-Mascheroni constant $\gamma$, Catalan constant $G$, Apery's constant $\zeta(3)$ appear a lot in the math context I read, they are closely related to Clausen functions $Cl_{2m}(x)$ and $Cl_{2m+1}(x)$, so if one could discover the closed-form expression of $Cl_{m}(x)$ then all mysteries would be gone. Up to now, clearly no new "magical" constant like $\pi$ has been found and the $Cl_{m}(x)$ remains itself as an integral unlike their counterpart $Sl_{m}(x)$, which was "solved" completely.
The question is why $Cl_{m}(x)$ and $Sl_{m}(x)$ are very much alike (to me) but we only know well one of them, more like "half of the world has gone missing". Does a god-tier constant (like siblings of $\pi$) exist to help solve the problem or things will remain as mysterious as they have been?
[Excuse my bad writing, I know the context is quite vague but really, I have always wanted to ask this question]
