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Lerch's Theorem


If there are two functions F_1(t) and F_2(t) with the same integral transform

 T[F_1(t)]=T[F_2(t)]=f(s),
(1)

then a null function can be defined by

 delta_0(t)=F_1(t)-F_2(t)
(2)

so that the integral

 int_0^adelta_0(t)dt=0
(3)

vanishes for all a>0.


See also

Null Function

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Cite this as:

Weisstein, Eric W. "Lerch's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LerchsTheorem.html

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