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A091477 Decimal expansion of (3*Catalan*Pi)/4 - Pi^3/64 + (Pi^2*log(64))/64 - (105*zeta(3))/64.

%I A091477 #20 Feb 16 2025 08:32:52
%S A091477 3,4,2,9,4,7,4,4,9,8,1,6,8,3,1,4,7,5,1,8,6,8,7,3,4,5,1,4,2,1,1,7,5,4,
%T A091477 1,5,6,3,6,9,1,9,3,1,6,0,9,4,0,4,0,4,1,3,2,2,1,8,3,0,2,8,4,0,5,9,9,4,
%U A091477 7,5,9,3,7,3,9,2,8,1,2,0,4,5,8,2,4,4,1,1,8,7,5,7,5,2,7,1,6,2,3,1,4,7
%N A091477 Decimal expansion of (3*Catalan*Pi)/4 - Pi^3/64 + (Pi^2*log(64))/64 - (105*zeta(3))/64.
%H A091477 G. C. Greubel, <a href="/A091477/b091477.txt">Table of n, a(n) for n = 0..10000</a>
%H A091477 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DefiniteIntegral.html">Definite Integral</a>
%F A091477 Equals Integral_{t=0..Pi/4} t^3/sin(t)^2 dt.
%e A091477 0.342947449816831475186873451421175415636919316094040413221830284...
%t A091477 RealDigits[(48*Catalan*Pi - Pi^3 + Pi^2*Log[64] - 105*Zeta[3])/64, 10, 100][[1]] (* _G. C. Greubel_, Aug 25 2018 *)
%o A091477 (PARI) default(realprecision, 100); (48*Catalan*Pi - Pi^3 + Pi^2*log(64) - 105*zeta(3))/64 \\ _G. C. Greubel_, Aug 25 2018
%o A091477 (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); L:=RiemannZeta();  (48*Catalan(R)*Pi(R) - Pi(R)^3 + Pi(R)^2*Log(64) - 105*Evaluate(L,3))/64; // _G. C. Greubel_, Aug 25 2018
%Y A091477 Cf. A000796, A002117, A006752, A016687.
%K A091477 nonn,cons
%O A091477 0,1
%A A091477 _Eric W. Weisstein_, Jan 13 2004