I would like to integrate the following expression with N being Integer
Integrate[(1 + Cos[f (1 + 2 n) \[Pi]])/(1 + Cos[f \[Pi]]), {f, 3, 10},
{Element[n, Integers]}]
Unfortunately the line above does not make sense in the interpreter.
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3$\begingroup$ Could you write exactly what is your domain, because first N is reserved to Numerical evaluation and there is no N in the function. $\endgroup$– cyrille.piateckiCommented May 24, 2016 at 17:51
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$\begingroup$ a = 1; b = 2; c = 10; FullSimplify[Integrate[(a + Cos[f (a + b c) [Pi]])/(a + Cos[f [Pi]]), {f, 3, 10}], Element[{a, b, c}, Integers]] $\endgroup$– user9660Commented May 24, 2016 at 18:04
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$\begingroup$ @Anonymous please verify the edit I made is correct. With the fix it (Incorrectly I think) reports that it does not converge. $\endgroup$– george2079Commented May 24, 2016 at 18:24
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1 Answer
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Here is a simple answer
Define k[n] as a listable function :
SetAttributes[k, Listable]
k[n_] := \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(3\), \(10\)]\(
\*FractionBox[\(1 + Cos[f\ \((1 + 2\ n\ )\)\ \[Pi]]\), \(1 +
Cos[f\ \[Pi]]\)] \[DifferentialD]f\)\)
then define a list compose of integer of the desired Length --- say 10
nn = Range[10]
ask for
k[nn]
On my computer it takes a little more than 25s.
answered May 24, 2016 at 18:56
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$\begingroup$ then run
FindSequenceFunctionon the result.. $\endgroup$ Commented May 24, 2016 at 19:13