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A294518
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Decimal expansion of 3*log(2) - Pi/2.
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1
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5, 0, 8, 6, 4, 5, 2, 1, 4, 8, 8, 4, 9, 3, 9, 3, 0, 9, 0, 2, 0, 3, 7, 4, 6, 7, 2, 7, 3, 4, 7, 7, 8, 2, 6, 2, 1, 2, 7, 9, 1, 5, 7, 0, 3, 3, 9, 3, 2, 1, 2, 8, 5, 1, 8, 7, 4, 5, 6, 7, 7, 3, 2, 3, 2, 6, 2, 7, 2, 6, 6, 2, 7, 6, 5, 9, 7, 9, 6, 4, 7, 5, 0, 3, 5, 7, 2, 5, 6, 8, 3, 1, 8, 1, 9, 7, 5, 2, 8, 6
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OFFSET
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0,1
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COMMENTS
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This is the value of the series V(4,3) = lim_{n->oo} V(4,3;n) with the partial sums V(4,3;n) = Sum_{k=0..n} 1/((k + 1)*(4*k + 3)) = Sum_{k=0..n} 1/A033991(k+1) = Sum_{k=0..n} (4/(4*k + 3) - 1/(k+1)) = A294516(n)/A294517(n).
In the Koecher reference v_4(3) = (1/4)*V(4,3) = (3/4)*log(2) + Pi/8 = 0.1271613037212348272550...
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REFERENCES
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Max Koecher, Klassische elementare Analysis, Birkhäuser, Basel, Boston, 1987, pp. 189-193.
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LINKS
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FORMULA
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V(4,3) = 3*log(2) - Pi/2.
Equals Sum_{k>=2} zeta(k)/4^(k-1). - Amiram Eldar, May 31 2021
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EXAMPLE
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0.5086452148849393090203746727347782621279157033...
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MATHEMATICA
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RealDigits[3*Log[2] - Pi/2, 10, 100][[1]] (* Amiram Eldar, May 31 2021 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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