There is a brilliant post about divergent series, generalized Abel summation (conformal summation), zeta summation and non-trivial mappings that can be discovered by looking at series:
http://cornellmath.wordpress.com/2007/07/28/sum-divergent-series-i/
http://cornellmath.wordpress.com/2007/07/30/sum-divergent-series-ii/
http://cornellmath.wordpress.com/2007/08/02/sum-divergent-series-iii/
Highly recommend this reading.
http://cornellmath.wordpress.com/2007/07/28/sum-divergent-series-i/
http://cornellmath.wordpress.com/2007/07/30/sum-divergent-series-ii/
http://cornellmath.wordpress.com/2007/08/02/sum-divergent-series-iii/
Highly recommend this reading.
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