On the nonmonotonicity of \((|Im(z^n)|)\) (Q1306703)
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scientific article; zbMATH DE number 1347936
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the nonmonotonicity of \((|Im(z^n)|)\) |
scientific article; zbMATH DE number 1347936 |
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On the nonmonotonicity of \((|Im(z^n)|)\) (English)
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11 May 2000
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The main result of this paper is that the sequence \(\{|r^n\sin \pi(na-b)|\}_{n=1}^\infty\) increases and decreases infinitely often (each event occurs with positive probability) unless special conditions are met. The proof is based on Weyl's uniform distribution theorem.
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sequence
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probability
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oscillation
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Weyl's uniform distribution theorem
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0.8381853
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0.8329278
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0.8325011
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0.8305304
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0.8282418
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0.8254464
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0.8249624
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