A378130 Decimal expansion of 24*L^2/(5^(7/4)*Pi^2), where L is the lemniscate constant (A062539).

9, 9, 9, 9, 9, 6, 3, 8, 3, 1, 5, 9, 0, 8, 4, 1, 2, 7, 7, 7, 2, 7, 6, 3, 4, 9, 9, 1, 8, 4, 7, 0, 6, 1, 1, 2, 8, 0, 8, 9, 4, 3, 4, 8, 8, 7, 7, 0, 3, 5, 9, 6, 6, 1, 3, 2, 9, 0, 9, 5, 9, 5, 0, 4, 9, 2, 6, 8, 1, 5, 2, 7, 3, 9, 9, 2, 1, 6, 4, 9, 2, 2, 9, 9, 3, 7, 4, 7, 9, 1

Offset: 0

Author

Paolo Xausa, Nov 18 2024

Keywords

• nonn
• cons
• easy

Examples

			0.999996383159084127772763499184706112808943488770...
		

Links

• Wikipedia, Lemniscate constant (includes this constant).
• Index to sequences related to the Gamma function.

Crossrefs

Cf. A008977, A062539, A091670.

Cf. A377999, A378128, A378129, A378129, A378131, A378132.

Programs

Mathematica

First[RealDigits[12*Pi/(5^(7/4)*Gamma[3/4]^4), 10, 100]] (* or *)
First[RealDigits[Sum[((-1)^k/6635520^k)*(4*k)!/k!^4, {k, 0, Infinity}], 10, 100]] (* or *)
First[RealDigits[HypergeometricPFQ[{1/4, 1/2, 3/4}, {1, 1}, -1/25920], 10, 100]]

Formula

Equals 12*Pi/(5^(7/4)*Gamma(3/4)^4) = 12*A091670/5^(7/4).

Equals Sum_{k >= 0} ((-1)^k/6635520^k)*(4*k)!/(k!)^4 = Sum_{k >= 0} ((-1)^k/6635520^k)*A008977(k).

Equals pFq(1/4, 1/2, 3/4; 1, 1; -1/25920), where pFq is the generalized hypergeometric function.