If there are two functions 
and 
with the same integral transform
![T[F_1(t)]=T[F_2(t)]=f(s),](/images/equations/LerchsTheorem/NumberedEquation1.svg) |
(1)
|
then a null function can be defined by
 |
(2)
|
so that the integral
 |
(3)
|
vanishes for all 
.
Lerch's Theorem
See also
Null FunctionExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Lerch's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LerchsTheorem.html