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We have the $j$-invariant defined as I have that $$ j(\tau)=\frac{1}{q}+\sum_{k\geq 0}c_kq^k, $$ where $q=e^{-2\pi t}$ ($\tau=it$) and $c_k\sim e^{4\pi\sqrt{k}}/(k^{3/4}\sqrt{2})$. The inversion ...

Consider the following formula which defines a piece-wise function which I believe corresponds to a series representation for the Dirac delta function $\delta(x)$. The parameter $f$ is the evaluation ...