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I would like to know the analytical expression for the following series (if it exists):

$\sum_{n=0}^{\infty} \frac{1}{n!} a^n b^{n^2}$

Does anybody have a clue on how to proceed?

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There have been questions on $\sum_{n \ge 0} x^{n^2}$ and similar lacunary series here. Such functions have singularities that are dense on the boundary of the circle of convergence, and can't be extended outside.

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  • $\begingroup$ Thanks..but I don't see any relevant question that might help me. $\endgroup$ – JFNJr Mar 18 '13 at 19:56

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