A381028 Decimal expansion of Sum_{k>=1} zeta(2k)/((2k-1)*2^(2k)).
4, 3, 7, 6, 5, 8, 2, 4, 2, 3, 1, 1, 2, 6, 1, 0, 9, 3, 3, 1, 5, 9, 2, 0, 9, 2, 6, 4, 3, 8, 0, 5, 1, 4, 0, 1, 6, 4, 8, 4, 3, 5, 6, 4, 5, 3, 5, 2, 3, 0, 6, 9, 6, 8, 3, 0, 2, 7, 1, 5, 6, 1, 3, 1, 5, 1, 3, 3, 2, 3, 4, 3, 5, 7, 1, 5, 8, 9, 4, 1, 7, 2, 4, 1, 6, 0, 1, 6, 8, 3, 9, 4, 9, 8, 3, 0, 9, 8, 5, 4, 2, 3, 9, 3, 1
Offset: 0
Examples
0.4376582423112610933159209...
Links
- H. M. Srivastava, M. L. Glasser, and V. S. Adamchik, Some definite integrals associated with the Riemann Zeta Function, Z. Anal. Anw. 19 (3) (2000) 831-846, (2.18) at n=0.
Programs
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Maple
evalf(Sum(Zeta(2*k)/((2*k-1)*4^k), k = 1 .. infinity), 105) # Amiram Eldar, Feb 15 2025
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Mathematica
RealDigits[NSum[Zeta[2*k]/((2*k - 1)*4^k), {k, 1, Infinity}, WorkingPrecision -> 120, NSumTerms -> 200]][[1, 1 ;; 105]] (* Amiram Eldar, Feb 15 2025 *) -
PARI
sumpos(k=1, zeta(2*k)/((2*k-1)*2^(2*k))) \\ Michel Marcus, Feb 13 2025
Formula
4*this = 1.75063296924504437... = Sum_{k>=1} (1/k)*log((2k+1)/(2k-1)).
Equals Sum_{k>=1} arctanh(1/(2*k))/(2*k) = Sum_{k>=1} arccoth(2*k)/(2*k). - Amiram Eldar, Feb 15 2025
Extensions
More terms from Amiram Eldar, Feb 15 2025
Comments