A363117 Decimal expansion of Product_{k>=1} (1 - exp(-7*Pi*k)).

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Formula

Equals exp(7*Pi/24) * Gamma(1/4) * ((sqrt(5 - sqrt(7)) - sqrt(3*sqrt(7) - 7)) * (2^(1/4) * sqrt(5 + sqrt(7)) + (56 + 23*sqrt(7))^(1/4)))^(1/4) / (2^(19/16) * 7^(7/16) * Pi^(3/4)).

Example

0.999999999718573154172243658382901236462919560257076490298122086100117...

Mathematica

RealDigits[E^(7*Pi/24) * Gamma[1/4] * ((Sqrt[5 - Sqrt[7]] - Sqrt[3*Sqrt[7] - 7]) * (2^(1/4) * Sqrt[5 + Sqrt[7]] + (56 + 23*Sqrt[7])^(1/4)))^(1/4) / (2^(19/16) * 7^(7/16) * Pi^(3/4)), 10, 120][[1]]
RealDigits[QPochhammer[E^(-7*Pi)], 10, 120][[1]]

Crossrefs

Cf. A259148 phi(exp(-Pi)), A259149 phi(exp(-2*Pi)), A292888 phi(exp(-3*Pi)), A259150 phi(exp(-4*Pi)), A292905 phi(exp(-5*Pi)), A363018 phi(exp(-6*Pi)), A259151 phi(exp(-8*Pi)), A363118 phi(exp(-9*Pi)), A363019 phi(exp(-10*Pi)), A363081 phi(exp(-11*Pi)), A363020 phi(exp(-12*Pi)), A363178 phi(exp(-13*Pi)), A363119 phi(exp(-14*Pi)), A363179 phi(exp(-15*Pi)), A292864 phi(exp(-16*Pi)), A363120 phi(exp(-18*Pi)), A363021 phi(exp(-20*Pi)).

Sequence in context: A361352 A363018 A269351 * A116667 A259151 A270172

Adjacent sequences: A363114 A363115 A363116 * A363118 A363119 A363120

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 15 2023

Status

approved