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Search: id:A128506
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| A128506 |
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Numerators of partial sums for a series for 3*sqrt(2)*(Pi^3)/2^7. |
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+0
3
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| 1, 28, 3473, 1187864, 32115203, 42776591068, 93938569006771, 93911487925744, 461478538827646397, 3165730339378740709148, 452199680641199918039, 5501473517781557885536888, 687727017229797976494536483
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OFFSET
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0,2
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COMMENT
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The denominators are given in A128507.
The limit n -> infinity of the rationals r(n) defined below is 3*sqrt(2)*(Pi^3)/2^7 = 1.027756...
This series is obtained from the Fourier series for y(x)= x*(Pi-x) if 0<=x<=Pi and y(x)= (Pi-x)*(2*Pi-x) if Pi<=x<=2*Pi evaluated at x=Pi/4.
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LINKS
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W. Lang, Rationals and limit.
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FORMULA
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a(n)=numerator(r(n)) with the rationals r(n):=sum(S(2*k,sqrt(2))/(2*k+1)^3,k=0..n) with Chebyshev's S-Polynomials S(2*k,sqrt(2))=[1,1,-1,-1] periodic sequence with period 4. See A057077.
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EXAMPLE
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Rationals r(n): [1, 28/27, 3473/3375, 1187864/1157625, 32115203/31255875,...].
3*sqrt(2)*(Pi^3)/2^7 = 1/1^3 + 1/3^3 - 1/5^3 - 1/7^3 + 1/9^3 + 1/11^3 - 1/13^3 - 1/15^3 + ...
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CROSSREFS
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Sequence in context: A103660 A107444 A061787 this_sequence A036525 A131315 A099058
Adjacent sequences: A128503 A128504 A128505 this_sequence A128507 A128508 A128509
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Apr 04 2007
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