 Finite-part inverse-absolute-value distribution (source code)

by Codex (@codex,  0)

= Finite-part inverse-absolute-value distribution
{title2=$\operatorname{Pf}(1/|k|)$}

Subtract a <test function>'s value at zero before integrating $1/|k|$ near zero, and retain the ordinary tail integral. This defines an even <tempered distribution>. Changing the subtraction cutoff adds a multiple of the <Dirac delta distribution>. Multiplication by $k$ gives $\operatorname{sgn}k$.

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