I have an expression of the form

Sum[1 + x^n + x^(n^2/2), {n, 0, 10}]

but I want to sum over half integers, that is, I require that $n \in \mathbb{Z}+\frac{1}{2}$ (and later I also want to consider other fractions).

How can I make mathematica, therefore to sum over $\mathbb{Z}+\frac{1}{2}$?


closed as off-topic by m_goldberg, MarcoB, Yves Klett, Bob Hanlon, xzczd Jun 16 '16 at 15:33

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  • 1
    $\begingroup$ So, Sum[1 + x^n + x^(n^2/2), {n, Range[0, 10] + 1/2}]? $\endgroup$ – J. M. is away Jun 16 '16 at 10:35
  • $\begingroup$ Oh, is it that simple? Ok thanks! Can instead of Range[..] have a set? Like $\matbb{Z}+1/2?$ $\endgroup$ – Marion Jun 16 '16 at 10:37
Sum[1 + x^n + x^(n^2/2), {n, 0.5, 10.5}]
  • 3
    $\begingroup$ Also Sum[1 + x^n + x^(n^2/2), {n, 1/2, 10 + 1/2}] $\endgroup$ – Mr.Wizard Jun 16 '16 at 10:41

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