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

Author

Paolo Xausa, Nov 17 2024

Keywords

• nonn
• cons
• easy

Examples

			0.78318878541367355294389069379822205618042023154005...
		

Links

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

Crossrefs

Cf. A002388, A062539, A068465, A371855.

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

Programs

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]]

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.