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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: power series problem
Replies: 8   Last Post: Mar 21, 2012 8:13 AM

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kiru.sengal@gmail.com

Posts: 25
Registered: 12/7/05
Re: power series problem
Posted: Mar 20, 2012 10:23 PM
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On Mar 20, 10:09 pm, Robert Adams <robert.ad...@analog.com> wrote:
> Hello
>
> I am stuck trying to find an expansion for
>
> f(x) = exp(i*x*log(x))
>
> i = sqrt(-1), valid for x > 0 (hopefully!).
>

What do you mean by expansion? If you want the real and imaginary
parts:
= e^(ix) * e^log(x)
= x * e^(ix)
= x (cosx + i sin x)
= x cosx + i (x sin x)
^^^^^^ ^^^^^^^^
Re Im

It is not technically correct to say i=sqrt(-1) because -1 has two
square roots, and it is not entirely obvious how to define the
principal square root of a negative number.

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