Relation of the Cyclotomic Equation with the Harmonic and Derived Series
We associate some (old) convergent series related to definite integrals with the cyclotomic equation xm-1=0, for several natural numbers m; for example, for m=3, x3-1=(x-1)(1+x+x2) leads to ∫01dx(1/(1+x+x2))=π/(33)=(1-1/2)+(1/4-1/5)+(1/7-1/8)+⋯. In some cases, we express the results in terms of the...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2015/950521 |
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