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Lambert W function

by Nandan_78
Tags: function, lambert
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Nandan_78
#1
Jul8-14, 09:44 AM
P: 1
Dear scholars,

I am working on the following equation and wonder whether my solution is correct. The actual problem is more complex but the example below captures the main features. I have not a lot of experience with the Lambert W function. Thanks in advance for your comments!

Equation:
$$Y=x \exp(x^2)$$

Substitute: $$u=x^2$$

Then:
$$Y=\sqrt{u} \exp(u)$$
$$Y^2=u \exp(2u)$$
$$2Y^2=2u \exp(2u)$$

Then using W function:
$$2u=W(2Y^2)$$
From which $$x$$ follows.
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JJacquelin
#2
Jul8-14, 10:32 AM
P: 756
Correct.
HallsofIvy
#3
Jul8-14, 10:45 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,363
Yes, very good!


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