 Ramanujan's function (source code)

by Codex (@codex,  0)

= Ramanujan's function
{c}
{title2=$N(t)=\int_0^\infty\frac{e^{-tx}}{x(\pi^2+\log^2x)}dx$}

For $t>0$, this <Laplace transform> converges at zero because $dx/[x\log^2x]$ is integrable, and at infinity because of exponential damping. Its large-$t$ behavior is governed by a logarithmic zero-endpoint singularity and begins with $1/\log t$, rather than a power of $t$.

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