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How to get an out-multiplied product from Series?

Nils H
Posted 3 years ago

Hello everybody, it's my first question, so I'm thankful for any advice.

I want Mathematica to get me a series of some Sinh function, explicitly 

Series[2^(2k)*(Sinh[x/2])^(2k),{x,0,5}]

The "9" at the end is arbitrary. My problem is the result of the form

enter image description here

because I want to get the coefficients of this series using the SeriesCoefficient function. But I cannot find any way to get the result as

enter image description here

I hope somebody has an idea. Thanks ! :-)

Attachments:
for_question.nb
POSTED BY: Nils H
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Nils,

SeriesCoefficient[] works properly on the expression without distributing the term:

In[1]:= exp = Series[2^(2 k)*(Sinh[x/2])^(2 k), {x, 0, 5}];
Table[SeriesCoefficient[exp, n], {n, 1, 5}]

Out[1]= {0, 1/12 k x^(2 k), 0, (k (-1 + 5 k) x^(2 k))/1440, 0}

Am I misunderstanding your question?

Regards
POSTED BY: Neil Singer
Nils H
Nils H
Posted 3 years ago

Great idea to use Series. Seems that this works perfectly ! Tanks a lot ! :-)

Best, Nils

POSTED BY: Nils H

Workaround ( ? ) : Don't work with Series

ser = Series[2^(2 k)*(Sinh[x/2])^(2 k), {x, 0, 5}] // Normal // Expand
Coefficient[ser, x^(2 + 2 k)]
POSTED BY: Hans Dolhaine
Nils H
Nils H
Posted 3 years ago

Thanks for your answer!

My problem is, that then the coefficient I get using SeriesCoefficient[... , 2] returns the coefficient that belongs to x^2 and the coefficient than includes the x^{2k} which was multiplied out. If I give Mathematica a concrete k, lets say k=1, then everything works perfect. But I need, lets say the coefficient that belongs to x^{2+2k} as a function of k...

Best, Nils

POSTED BY: Nils H
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