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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