most recent 30 from http://mathoverflow.net 2013-05-21T05:13:25Z http://mathoverflow.net/feeds/user/18946 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/79731/sum-of-series-where-exponent-is-sum-of-arithmetic-progression edwin11 2011-11-01T17:39:54Z 2011-11-02T01:05:29Z

<p>Hi,</p> <p>How do i get the sum of such a sequence:</p> <p>$1 + x^{-1} + x^{-3} + x^{-6} + ...$</p> <p>where the exponents are actually sum of arithmetic progression. i.e.</p> <p>$x^{-0} + x^{-(0 + 1)} + x^{-(0 + 1 + 2)} + x^{-(0 + 1 + 2 + 3)} + ...$</p> <p>which can also be expressed as</p> <p>$\sum_{i=0}^{\infty} x^{-\frac{i(i + 1)}{2}}$</p> <p>?</p> <p>Thanks.</p>

http://mathoverflow.net/questions/79731/sum-of-series-where-exponent-is-sum-of-arithmetic-progression edwin11 2011-11-02T05:58:03Z 2011-11-02T05:58:03Z

i was solving a markov process equation when i ended up with such a series. from the looks of the complexity, it is much more possible that i got something wrong somewhere and ended up like that... (unfortunately i still couldn't figure out what went wrong...)