4
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In the help file, under BellB, I read at "Properties and Relations":

Sum can give results involving BellB:

Sum[k^n/k!, {k, 0, Infinity}]  
   E BellB[n]  

but, in my version 10.0.1.0 it does not do as claimed. Neither does Wolfram Alpha.

Question: did it work in previous versions?

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  • $\begingroup$ The example behave the same (i.e. does not return BellB) in v9 on Win 7. $\endgroup$ – bobthechemist Sep 21 '14 at 14:20
  • $\begingroup$ Works on v7.0.1 on a Mac but not v8, v9, or v10. $\endgroup$ – Bob Hanlon Sep 21 '14 at 15:31
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    $\begingroup$ Sum[k^n/k!, {k, 0, Infinity}, Assumptions -> {n [Element] Integers, n > 0}] returns E BellB[n] $\endgroup$ – ulvi Sep 21 '14 at 21:18
  • $\begingroup$ @ulvi: well done. It should be seen as an improvement over v7.0.1. Brings up the question of 'when do we obtain a conditional result' like Integrate[x^n, {x, 0, 1}] giving ConditionalExpression[(1 + n)^(-1), Re[n] > -1] ? $\endgroup$ – Wouter Sep 23 '14 at 8:10

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