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The notion of limiting sum cannot be expressed as a signature.
There is no notion of approximation with signatures, arbitrarily
close rational numbers can have arbitrarily different signatures.
Consequently, under our present knowledge of signatures, it does
not appear possible to compute signatures of definite integrals,
definite sums, limits and similar operations.
Additionally, integrals or summations with infinite limits are
completely outside the reach of signatures for an even stronger
reason.

*Gaston Gonnet*

*1999-07-04*