# Expansion of Expression

I am trying to expand out expressions that have several terms similar to

E[-lH] Sinh[l (H - h)]


The Expand command just gives me back the original expression. Even when I do a partial expansion, and then try Expand:

Expand[E[-l H] (E[l (H - h)] - E[-l (H - h)])]


I get back:

E[-H l] (-E[(h - H) l] + E[(-h + H) l])


From ExpandAll:

-E[-H l] E[h l - H l] + E[-H l] E[-h l + H l]


I would like E[-lH] Sinh[l (H - h)] to be expanded as:

E[-h l] - E[(h - 2 H)l]

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## 1 Answer

E is a constant, so either use it as E^(-H l)) or use Exp[-H l]. Then you can do :

Simplify[TrigToExp[Exp[-l H] Sinh[l (H - h)]]]
(* 1/2 (E^(-h l) - E^((h - 2 H) l)) *)

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Thanks, that did answer the question I asked. But when I tried: Simplify[TrigToExp[Exp[-l H] Sinh[l (H - h)] Sinh[l x]]], I get: 1/4 E^(l (h - 2 H - x)) (-1 + E^(2 (-h + H) l)) (-1 + E^(2 l x)). Is there a way to have this completely expanded out? – user1031565 Nov 29 '12 at 11:32
I get the fully expanded result with ExpandAll: ExpandAll[TrigToExp[Exp[-l H] Sinh[l (H - h)] Sinh[l x]]] gives: -(1/4) E^(-h l - l x) + 1/4 E^(h l - 2 H l - l x) + 1/4 E^(-h l + l x) - 1/4 E^(h l - 2 H l + l x) – user1031565 Nov 29 '12 at 12:41
Just use Expand[...] or equivalently ... //Expand. – b.gatessucks Nov 29 '12 at 12:41