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How can I separate two parts of power of exponential functions in Mathematica? I have an expression similar to this one:

a*b*Exp[u+v]+c*Exp[u]

I want to set Exp[v] to zero. For this target I need to expand Exp[u+v] to Exp[u]*Exp[v], then set Exp[v]-> 0. How can I expand Exp[u+v] to Exp[u]*Exp[v] in Mathematica?

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2 Answers 2

To get an actual mathematically valid result that corresponds to your goal, you should not rely on pattern substitutions because they are not guaranteed to obey the principles of mathematical sanity.

Instead, I would suggest you do the following:

Limit[a*b*Exp[u + v] + c*Exp[u], v -> -Infinity]

(* ==> c E^u *)

Here I simply used the fact that an exponential goes to zero when its exponent goes to negative infinity along the real axis. I could have used a rule instead, but the function Limit is designed for this purpose, so why not use it?

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Did you mean v -> -∞ rather than z? This answer would make a lot more sense if so... –  Oleksandr R. May 24 at 3:12
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@OleksandrR. How did you guess? I really was hoping nobody would be able to understand this answer. –  Jens May 24 at 4:16

It depends on your ultimate aim. If it is only to look at, you might use this function:

    factorExp[expr_] := Times @@ Map[HoldForm[E^#] &, List @@ expr[[2]]]

The action is like follows:

Exp[(x - y)^2 + b*Sqrt[u - v] + a + x + y^m + z^3] // factorExp

Try it. However, each term is held, and as soon as you try to release hold the terms fuse for a well-known reason. So it is not for further use in the calculations, if any.

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