User:Sintel/Zeta working page: Difference between revisions
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== Choice of sigma == | == Choice of sigma == | ||
{{todo|inline=1|text=This section is incomplete! Discuss symmetry and add some conclusion}} | {{todo|complete section|inline=1|text=This section is incomplete! Discuss symmetry and add some conclusion}} | ||
The infinite sum derived above converges only when <math>\mathrm{Re}(s) = \sigma > 1</math>. However, mathematicians found that the zeta function can be "extended" or "continued" to other values of s where the original sum doesn't converge. This mathematical technique is called {{w|analytic continuation}}. | The infinite sum derived above converges only when <math>\mathrm{Re}(s) = \sigma > 1</math>. However, mathematicians found that the zeta function can be "extended" or "continued" to other values of s where the original sum doesn't converge. This mathematical technique is called {{w|analytic continuation}}. | ||
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== Zeta lists == | == Zeta lists == | ||
{{todo|inline=1|text=add the original lists back here, and discuss their relevance.}} | {{todo|complete list|inline=1|text=add the original lists back here, and discuss their relevance.}} | ||
== Optimal octave stretch == | == Optimal octave stretch == | ||