= Logarithmic expansion of Ramanujan's function
{title2=$N(t)\sim\sum_{n\ge0}c_n(\log t)^{-n-1},\quad\sum_{n\ge0}c_nz^n/n!=1/\Gamma(1-z)$}
The <Gamma reflection formula> gives $(\sin\pi z/\pi)\Gamma(z)=1/\Gamma(1-z)$, analytic at zero with value one. A finite-parameter <Watson's lemma> representation of <Ramanujan's function> therefore gives the displayed coefficients. In particular $c_0=1$, $c_1=-\gamma$ and $c_2=\gamma^2-\pi^2/6$, with $\gamma$ <Euler's constant>. Obtaining this representation requires taking an imaginary part before sending its Mellin exponent to zero; the original complex <integral> is divergent at that boundary.
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