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

0,1

Links

Table of n, a(n) for n=0..89.

Wikipedia, Lemniscate constant (includes this constant).

Index to sequences related to the Gamma function.

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.

Example

0.999996383159084127772763499184706112808943488770...

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]]

Crossrefs

Cf. A008977, A062539, A091670.

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

Sequence in context: A346570 A288238 A100547 * A259150 A292826 A346435

Adjacent sequences: A378127 A378128 A378129 * A378131 A378132 A378133

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 18 2024

Status

approved