Manuscript IX-E-2@1 · IX-E-2.tex · section · e70d9077

The sine distribution

Common-regulator evaluation › The sine distribution · lines 769–784

IX-E-2@1#eq:D-regulated

The companion calculation is

D_{ε} (v, R) = \frac{1}{2 π ^{2} R} \int_{0}^{\infty} e^{- εq} sin (q R) sin (q v) d q = \frac{1}{4 π ^{2} R} [\frac{ε}{ε ^{2} + ( R - v ) ^{2}} - \frac{ε}{ε ^{2} + ( R + v ) ^{2}}] .

Displayed formulas in this passage

IX-E-2@1#eq:D-regulated · line 772
$D_{ε} (v, R) = \frac{1}{2 π ^{2} R} \int_{0}^{\infty} e^{- εq} sin (q R) sin (q v) d q = \frac{1}{4 π ^{2} R} [\frac{ε}{ε ^{2} + ( R - v ) ^{2}} - \frac{ε}{ε ^{2} + ( R + v ) ^{2}}] .$