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If I interpolate a list

 f=ListInterpolation[{1,2,3,4,5,6,7}]

the result is in the domain {{1,7}}, so something like f[8] will be out of scope.

How can I shift the domain, say from 1,7 to 8,15?

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One thing you can do is to shift the function:

f = ListInterpolation[{1, 2, 3, 4, 5, 6, 7}]
g[x_] := f[x - 7];

Now g is a shifted version of f having the domain starting at 8.

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  • $\begingroup$ Or to get a periodic function: g[x_] := Mod[x, 7] /. (0 -> 7) $\endgroup$ – Bob Hanlon Jul 4 '18 at 14:35
  • $\begingroup$ @BobHanlon If one is aiming for periodicity, there is the PeriodicInterpolation option $\endgroup$ – Lukas Lang Jul 4 '18 at 15:14
  • $\begingroup$ @LukasLang - if you try that option you will encounter the error ListInterpolation::per : In dimension 1 the data at the endpoints of the fundamental period are not equal. $\endgroup$ – Bob Hanlon Jul 4 '18 at 15:17

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