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A091477
Decimal expansion of (3*Catalan*Pi)/4 - Pi^3/64 + (Pi^2*log(64))/64 - (105*zeta(3))/64.
1
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, 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, 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
OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Definite Integral
FORMULA
Equals Integral_{t=0..Pi/4} t^3/sin(t)^2 dt.
EXAMPLE
0.342947449816831475186873451421175415636919316094040413221830284...
MATHEMATICA
RealDigits[(48*Catalan*Pi - Pi^3 + Pi^2*Log[64] - 105*Zeta[3])/64, 10, 100][[1]] (* G. C. Greubel, Aug 25 2018 *)
PROG
(PARI) default(realprecision, 100); (48*Catalan*Pi - Pi^3 + Pi^2*log(64) - 105*zeta(3))/64 \\ G. C. Greubel, Aug 25 2018
(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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jan 13 2004
STATUS
approved