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Series error: First argument is not a valid variable?

Posted 1 year ago

See my following testing:

In[140]:= Limit[(1+ I \[Theta]/x)^x,x->Infinity]/.{I \[Theta]->x}
Series[%, {x, 0, 10}]/.{x-> I \[Theta]}

Out[140]= E^x

During evaluation of In[140]:= SeriesData::sdatv: First argument I \[Theta] is not a valid variable.

Out[141]= SeriesData[Complex[0, 1] \[Theta], 0, {1, 1, 
Rational[1, 2], 
Rational[1, 6], 
Rational[1, 24], 
Rational[1, 120], 
Rational[1, 720], 
Rational[1, 5040], 
Rational[1, 40320], 
Rational[1, 362880], 
Rational[1, 3628800]}, 0, 11, 1]

Why will the "SeriesData::sdatv: First argument I [Theta] is not a valid variable." be triggered in this case, and how to fix it?

Regards, Zhao

POSTED BY: Hongyi Zhao
4 Replies
Posted 1 year ago

I see. Thank you for your detailed explanation.

POSTED BY: Hongyi Zhao
Posted 1 year ago

But you still use the same rule {x -> I [Theta]}, why can this problem be avoided?

POSTED BY: Hongyi Zhao

I used \[Theta] for the variable in Series. I used the replacement only on the function, that is, the first argument of Series. You used the replacement on the whole Series with the variable initially as x. Your use of the replacement causes the variable to become Times[I, θ]. Examine the difference in our codes carefully.

POSTED BY: Michael Rogers

You changed the variable x to I θ, which is Times[I, θ]. Variable cannot have the head Times.

I don't know how to fix it, because I am unsure what you wish to accomplish. However, the following avoids the error:

Series[% /. {x -> I \[Theta]}, {\[Theta], 0, 10}]
POSTED BY: Michael Rogers
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