Say I have

$A = c_1 (Log(a b))^2 + c_2 (Log(a))^2 + c_3 Log(a) + c_4$

Then, I can imagine expansion of terms in term of $Log(a)$:

$A= \{c_4 + c_1 (Log(b))^2\} + Log(a) \{ c_3 +2 c_1 Log(b)\} + (Log(a))^2\{c_1 + c_2\}$

Is there any ways to achieve this in Mathematica when I have a complicated expression in terms of $A$?


closed as off-topic by Daniel Lichtblau, garej, MarcoB, Itai Seggev, J. M. will be back soon Jul 28 '17 at 6:44

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  • "This question cannot be answered without additional information. Questions on problems in code must describe the specific problem and include valid code to reproduce it. Any data used for programming examples should be embedded in the question or code to generate the (fake) data must be included." – Daniel Lichtblau, garej, MarcoB, Itai Seggev
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  • 2
    $\begingroup$ This could be edited into a good self-anwered question. You would have to express both the problem and its answer in the Wolfram Language, not in MathJax. You would also have to give a example of how it would be used in a more complicated expression involving A As it stands, it is likely to be closed. $\endgroup$ – m_goldberg Jul 27 '17 at 22:07
  • $\begingroup$ We can reopen this if you edit into a proper self-answered question with relevant code. $\endgroup$ – J. M. will be back soon Jul 28 '17 at 6:44

Let $a = Exp[c],$ then $Log^n[a] = c^n,$ then do series expansion around $c=0$. Then expansion in $c$ is really, expansion in $Log[a]$.

  • $\begingroup$ Applying your procedure to A in the question would make your answer more effective. $\endgroup$ – bbgodfrey Jul 27 '17 at 16:53
  • $\begingroup$ Yeah, that is what I meant. I was just noting that c is Log[a]. $\endgroup$ – Quantization Jul 27 '17 at 18:23

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