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

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

Author

Eric W. Weisstein, Jan 13 2004

Keywords

• nonn
• cons

Examples

			0.342947449816831475186873451421175415636919316094040413221830284...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Definite Integral

Crossrefs

Cf. A000796, A002117, A006752, A016687.

Programs

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

Mathematica

RealDigits[(48*Catalan*Pi - Pi^3 + Pi^2*Log[64] - 105*Zeta[3])/64, 10, 100][[1]] (* G. C. Greubel, Aug 25 2018 *)

PARI

default(realprecision, 100); (48*Catalan*Pi - Pi^3 + Pi^2*log(64) - 105*zeta(3))/64 \\ G. C. Greubel, Aug 25 2018

Formula

Equals Integral_{t=0..Pi/4} t^3/sin(t)^2 dt.