[math]\sum _{k=0}^{\infty } \frac{17+i k}{6\ 2^k}=\frac{17}{3}+\frac{i}{3}[/math]
[math]\frac{1}{3} (3 \lambda -1)=1[/math]
[math]\lambda - 4/3 = 0[/math]
[math]1/3 (3 \lambda - 1) = 1[/math]
[math]\lambda \left(\frac{n}{2}\right)+\lambda (3 n+1)=-\frac{\left(1+2 \sum _{k=1}^{\infty } (-1)^k e^{\frac{1}{2} i \pi k^2 n}\right){}^4}{\left(1+2
\sum _{k=1}^{\infty } e^{\frac{1}{2} i \pi k^2 n}\right){}^4}-\frac{\left(1+2 \sum _{k=1}^{\infty } (-1)^k e^{i \pi k^2 (3 n+1)}\right){}^4}{\left(1+2
\sum _{k=1}^{\infty } e^{i \pi k^2 (3 n+1)}\right){}^4}+2[/math]
[math]\pi[\math] rather feels like the symbol even classical/ancient mathematics needed to associate a symbol concept of n-dimensions (will performing this calculation always exist/never end/is there an afterlife) to basically a PHYSICAL experience of three concepts that translate as : trying to measuring a circle in ratios and concluding all countable sets (the number 1). Or it's just a way to identify 'is my mouth also my asshole?'
So mathematicians whack in [math]\pi[\math] equations when it's, "Hey! You've matched this arbitrary quantum state of futility with permissibly when you utilize this minimally-identifiable non-destructive set!"
Or hello. Interesting times, oui?