A378129 Decimal expansion of log(L^2/Pi), where L is the lemniscate constant (A062539).

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

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 log(Pi^2/(2*Gamma(3/4)^4)) = log(A002388/(2*A068465^4)).

Equals 2*log(2*Gamma(5/4)/Gamma(3/4)) = 2*log(A371855/A068465).

Equals Integral_{x=0..oo} exp(-x)*tanh(x)/x dx.

Example

0.78318878541367355294389069379822205618042023154005...

Mathematica

First[RealDigits[Log[Pi^2/2/Gamma[3/4]^4], 10, 100]] (* or *)
First[RealDigits[Integrate[Exp[-x]*Tanh[x]/x, {x, 0, Infinity}], 10, 100]]

Crossrefs

Cf. A002388, A062539, A068465, A371855.

Cf. A377999, A378128, A378130, A378131, A378132.

Sequence in context: A394334 A153622 A257576 * A064207 A396823 A020843

Adjacent sequences: A378126 A378127 A378128 * A378130 A378131 A378132

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 17 2024

Status

approved