Sokhotsky's Formula

Let P(1/x) be a linear functional acting according to the formula

where phi in D and D is the space of test functions. Then Sokhotsky's formula states that

lim_(epsilon->0)1/(x+/-iepsilon)=∓ipidelta(x)+P(1/x),

(3)

where delta(x) is the delta function (Vladimirov 1971, pp. 75-76).

See also

Delta Function

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References

Vladimirov, V. S. Equations of Mathematical Physics. New York: Dekker, 1971.

Referenced on Wolfram|Alpha

Sokhotsky's Formula

Cite this as:

Weisstein, Eric W. "Sokhotsky's Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SokhotskysFormula.html

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