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A class of theories that attempt to explain all existing particles (including force carriers) as vibrational modes of extended objects, such as the 1-dimensional fundamental string.
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New series for $\pi$ from string theory
It is unlikely $S(1)$ has a closed form.
We have \begin{align}S(1)&=4\sum_{k\ge1}(-1)^k\binom{-1/(4k)}k\frac{2k}{2k+1}\end{align} and (substituting $\lambda=0$ in the original Saha-Sinha formula for $ …