Where have divergent infinite sums been successfully substituted for their corresponding Riemann Zeta results? (i.e $1+2+3\dots=-1/12$)

Asked Oct 04 '20 at 21:09

Active Oct 04 '20 at 22:10

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In this numberphile video Professor Frenkel states that divergent infinite sums have been substituted for their "finite parts" (i.e $-1/12$ for $1+2+3+\dots$) and yielded correct answers (that have then been justified in other ways). What are some examples of this?

edited Oct 04 '20 at 22:10

Alma Arjuna

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asked Oct 04 '20 at 21:09

Andrew Kynaston

1

Maybe this is better to ask in physics.se ? – GEdgar Oct 04 '20 at 21:13
1

You can see some reference here: https://math.stackexchange.com/questions/2170792/is-1234-cdots-frac112-the-unique-value-of-this-series – Emilio Novati Oct 04 '20 at 21:16

Where have divergent infinite sums been successfully substituted for their corresponding Riemann Zeta results? (i.e $1+2+3\dots=-1/12$)

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