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How to remove the mixed derivative when expanding Taylor series to O(1)

Posted 9 years ago

Hello !

I am a new user of mathematica and i am struggling with the Taylor (Mclaren) series. I want to expand the following multi variable function with respect to "xsi0" and "rho0" up to O(1) :

y1[z_] := (R + Subscript[\[Rho], 0] E^(I \[Gamma] z )) Cos[
\!\(\*SuperscriptBox[\(k\), \('\)]\) (z - 
       Subscript[\[Xi], 0] E^(I \[Gamma] z ))];

So I do :

y1e[z_] := 
 Series[y1[z], {Subscript[\[Xi], 0], 0, 1}, {Subscript[\[Rho], 0], 0, 
     1}] // Normal // Expand
y1e[z]

Which gives the correct expansion but a mixed derivative term is also included (which is technically a second order term). I would like to get rid of it. Is there a clean way to do so ?

POSTED BY: Can Selcuk
2 Replies

I didn't test my expand function extensively but it seems it works and can help you. You can also take a look at various links in the topic it was created in:

MMA.SE: Isolating cross terms

expand[
   y1[z], 
   "SmallTerms" -> {Subscript[\[Xi], 0], Subscript[\[Rho], 0]}
] //  Normal // Expand

enter image description here

POSTED BY: Kuba Podkalicki
Posted 9 years ago

Thank you, it worked like a charm,

Best

POSTED BY: Can Selcuk
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