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Diffstat (limited to 'source/know/concept/sokhotski-plemelj-theorem')
| -rw-r--r-- | source/know/concept/sokhotski-plemelj-theorem/index.md | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/source/know/concept/sokhotski-plemelj-theorem/index.md b/source/know/concept/sokhotski-plemelj-theorem/index.md index 445b029..e139954 100644 --- a/source/know/concept/sokhotski-plemelj-theorem/index.md +++ b/source/know/concept/sokhotski-plemelj-theorem/index.md @@ -10,7 +10,7 @@ layout: "concept" --- The goal is to evaluate integrals of the following form, -where $$f(x)$$ is assumed to be continuous in the integration interval $$[a, b]$$: +where $$f(x)$$ is real and continuous in the integration interval $$[a, b]$$: $$\begin{aligned} \lim_{\eta \to 0^+} \int_a^b \frac{f(x)}{x + i \eta} \dd{x} @@ -56,7 +56,7 @@ $$\begin{aligned} &= \lim_{m \to +\infty} \frac{\pi}{\pi} \int_a^b \frac{m}{1 + m^2 x^2} f(x) \dd{x} \end{aligned}$$ -The expression $$m / \pi (1 + m^2 x^2)$$ is a so-called *nascent delta function*, +The expression $$m / (\pi (1 + m^2 x^2))$$ is a so-called *nascent delta function*, meaning that in the limit $$m \to +\infty$$ it converges to the [Dirac delta function](/know/concept/dirac-delta-function/) $$\delta(x)$$: |