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Search: id:A137218
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| A137218 |
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Decimal expansion of the argument of -1+i2. |
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+0
1
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| 2, 0, 3, 4, 4, 4, 3, 9, 3, 5, 7, 9, 5, 7, 0, 2, 7, 3, 5, 4, 4, 5, 5, 7, 7, 9, 2, 3, 1, 0, 0, 9, 6, 5, 8, 4, 4, 1, 2, 71, 2, 1, 7, 5, 3, 9, 7, 3, 6, 7, 3
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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Gives closed forms for many arctangent values.
ArcTan[2]=Pi-a ArcTan[1/2]=a-Pi/2
ArcTan[3]=a-Pi/4 ArcTan[1/3]=3Pi/4-a
ArcTan[7]=7Pi/4-2a ArcTan[1/7]=2a-5Pi/4
ArcTan[4/3]=2a-Pi ArcTan[3/4]=3Pi/2-2a
ArcTan[GoldenRatio]=a/2
There is the sum
a=Sum[((2+8r)/(8n+1)+(1-8r)/(8n+2)-4r/(8n+3)-(1+8r)/(8n+4)-(1/2+2r)/(8n+5)-(3/4+2r)/(8n+6)+r/(8n+7))/16^n,n,1,Infinity]
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FORMULA
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a=Pi-ArcTan[2]
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EXAMPLE
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2.0344439357957027354455779231...
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CROSSREFS
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Adjacent sequences: A137215 A137216 A137217 this_sequence A137219 A137220 A137221
Sequence in context: A137372 A066439 A101336 this_sequence A087819 A066246 A109921
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KEYWORD
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cons,nonn
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AUTHOR
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Matt Rieckman (mjr162006(AT)yahoo.com), Mar 06 2008
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