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

Posted 8 years ago
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 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 ?
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Posted 8 years ago
 Thank you, it worked like a charm,Best
Posted 8 years ago
 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 