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Bug introduced in 10.0


Series does not correctly construct expansions of inactive Integrate:

Series[Inactive[Integrate][x^a, {x, 0, 1}], {a, 0, 2}]

enter image description here

It pulls stuff that depends on the integration variable x, outside of the integral.

Is there a workaround? Is this a bug, or intended behavior?

Edit: Reported as bug, case 3895925

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  • $\begingroup$ Well, it's incorrect, so I've got to think it's not intended. $\endgroup$ – Michael E2 May 26 '17 at 22:38
  • $\begingroup$ The problem is that due to Inactive the Series code treats the integral as any other function, hence takes derivatives of it. It is instructive to replace Integrate by f. $\endgroup$ – Bruno Le Floch May 27 '17 at 2:41
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A workaround

taylor[f_, x_List, x0_List, n_Integer] := 
 Sum[1/i! Nest[(x - x0).# &, D[f, {x, i}] /. Thread[x -> x0], i], {i, 0, n}]

taylor[Inactive[Integrate][x^a, {x, 0, 1}], {a}, {0}, 2]

enter image description here

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