[seqfan] Re: Closed form?

Robert Israel israel at math.ubc.ca
Wed Apr 29 18:39:34 CEST 2009


I don't know, but the Laplace transform of this is
F(s) = sum_{k=0}^infty 2^(-(k^2-k)/2) s^(-1-k)
which can be expressed in terms of Jacobi theta functions.

Cheers,
Robert Israel

On Wed, 29 Apr 2009, David Wilson wrote:

> Is there a closed form for
>
> f(x) = SUM(k = 0 to inf; x^k/(2^((k^2-k)/2)*k!)))
>
> i.e;
>
> f(x) = 1 + x + x^2/4 + x^3/48 + x^4/1536 + x^5/122880 + ...
>
>
>
>
>
>
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