A380908 Decimal expansion of lim_{s->1} (zeta(s) - Pi^(s/2)/((s-1)*Gamma(s/2))) (negated).
9, 7, 6, 9, 0, 4, 2, 9, 1, 0, 3, 3, 8, 7, 8, 9, 6, 6, 1, 8, 5, 6, 8, 9, 7, 5, 2, 0, 9, 3, 5, 0, 4, 7, 0, 8, 3, 7, 8, 0, 6, 7, 8, 7, 2, 8, 4, 7, 9, 4, 9, 2, 4, 0, 4, 7, 4, 6, 0, 7, 9, 2, 7, 7, 8, 7, 0, 2, 8, 6, 4, 3, 5, 2, 3, 2, 7, 5, 4, 2, 0, 0, 2, 9, 2, 0, 1, 4, 3, 0, 4, 8, 8, 2, 9
Offset: 0
Examples
-0.976904291033878966185689752093504708378...
Links
- Paolo Xausa, Table of n, a(n) for n = 0..10000
- David Loeffler and Michael Stoll, Formalizing zeta and L-functions in Lean, arXiv:2503.00959 [math.NT], March 2025.
- Mathlib4, Value of the completed Riemann zeta at s = 1.
- Wikipedia, Lean (proof assistant), March 2025.
Programs
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Maple
c := -(gamma - log(4*Pi))/2: evalf(c, 110)*10^95: ListTools:-Reverse(convert(floor(%), base, 10));
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Mathematica
First[RealDigits[(EulerGamma - Log[4*Pi])/2, 10, 100]] (* Paolo Xausa, Mar 05 2025 *)
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PARI
(Euler-log(4*Pi))/2 \\ Charles R Greathouse IV, Sep 03 2025
Comments