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I have two lists: the first is {t,f[t]} and the second {t,l[t]}.

What i need is the first order expansion of f[t] in l[t]:

$f(t)\sim f(t)\vert_{l(0)}+\int_{0}^{t}d\tau\; l(\tau)\;\frac{\partial f(t)}{\partial l(\tau)}\big\vert_{l(0)}+\dots$

There is a way to do it?

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  • $\begingroup$ Have you considered replacing f[t] with f[InverseFunction[l][s]] and working from there? $\endgroup$ – Pillsy Apr 9 '17 at 18:20
  • $\begingroup$ Might get better responses if actual lists are posted. $\endgroup$ – Daniel Lichtblau Apr 9 '17 at 20:04
  • $\begingroup$ Daniel the lists are very long, how can i post them? $\endgroup$ – Kowalski Apr 9 '17 at 20:34
  • $\begingroup$ Then try to find shorter lists, or come up with a representative subset of your actual lists. $\endgroup$ – J. M. will be back soon Apr 9 '17 at 23:16

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