A363019 Decimal expansion of Product_{k>=1} (1 - exp(-10*Pi*k)).

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

Offset

0,1

Links

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

Formula

Equals exp(5*Pi/12) * Gamma(5/4) * sqrt(2*(sqrt(5) - 1)/5) / Pi^(3/4).

Equals A292905 * A292904.

Example

0.999999999999977288989316758545823200993325029482707067413205453362995...

Mathematica

RealDigits[E^(5*Pi/12)*Gamma[5/4]*Sqrt[2*(Sqrt[5] - 1)/5]/Pi^(3/4), 10, 120][[1]]
RealDigits[QPochhammer[E^(-10*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)), A363117 phi(exp(-7*Pi)), A259151 phi(exp(-8*Pi)), A363118 phi(exp(-9*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: A332550 A137577 A363118 * A363081 A363020 A363178

Adjacent sequences: A363016 A363017 A363018 * A363020 A363021 A363022

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 13 2023

Status

approved