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Lerch's Theorem

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

{\mathcal T}[F_1(t)] = {\mathcal T}[F_2(t)] \equiv f(s),
\end{displaymath} (1)

then a Null Function can be defined by
\delta_0(t) \equiv F_1(t)-F_2(t)
\end{displaymath} (2)

so that the integral
\int^a_0 \delta_0(t)\,dt = 0
\end{displaymath} (3)

vanishes for all $a > 0$.

See also Null Function

© 1996-9 Eric W. Weisstein