Nma1242012-01-03 15:13:00

hello; this is mma 5.0

I am having hard time figuring how to tell mma to convert the

output to a form I want.

In Maple, I can use the ‘convert’ command, which is really nice, but

mma has no such command to convert an expression between different

forms. So other than using Simplify, FullSimplify, ExpToTrig, TrigToExp,

I have no idea what to do.

This is an example, the result of this I want to be expressed as

arcsinh(y/c), not in the way it is generated, (which is correct

but different form).

So I guess I am asking one general question: What is the mma command

that is eqivelant to maple ‘convert’? and a specific question is how

to make the output of this example expressed in arcsinh instead of in

terms of ln?

— mma code —–

In[4]:= sol = Integrate[1/Sqrt[c^2+y^2],y]

2 2

Out[4]= Log[y + Sqrt[c + y ]]

In[5]:= Simplify[sol,Elements[c,Reals]]

2 2

Out[5]= Log[y + Sqrt[c + y ]]

—- maple code —–

In maple, in this example I did not have to use the convert

command, but in other examples I used it.

assume(c,real);

/ 1 \1/2

sol := arcsinh(|—-| y)

| 2 |

\ c /

Now I can if needed convert the above to ln using convert:

Dan2012-01-03 15:13:05

In Mma, if I make the assumption that c>0, I can not show that both are

equal.

Did I type the second equation correctly?

$Assumptions = c > 0;

v1 = FullSimplify[Integrate[1/Sqrt[c^2 + y^2], y]] Log[y + Sqrt[c^2 + y^2]]

v2 = FullSimplify[TrigToExp[ArcSinh[y*Sqrt[1/c^2]]]] Log[(y + Sqrt[c^2 + y^2])/c]

—

Dana DeLouis

Using Windows XP & Office XP

= = = = = = = = = = = = = = = = =

Ken pledger2012-01-03 15:13:27

I can’t help you with mma, but your question may be essentially

mathematical: how can you express a log in terms of an inverse sinh?

If that’s it, then in the definition

sinh(u) = (e^u – e^-u)/2

write u = ln(t) so e^u = t.

Then sinh(ln(t)) = (t – (1/t))/2

so ln(t) = arcsinh((t – (1/t))/2).

That should enable you to make the conversions you want, just by

plugging in different values of t.

Ken Pledger.

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