A363021 - OEIS

A363021

Decimal expansion of Product_{k>=1} (1 - exp(-20*Pi*k)).

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

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OFFSET

0,1

LINKS

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

FORMULA

Equals exp(5*Pi/6) * Gamma(1/4) * (5^(1/4) - 1) * sqrt((sqrt(5) - 1)/5) / (2^(19/8) * Pi^(3/4)).

EXAMPLE

0.999999999999999999999999999484209993745715964958151977112711625102369...

MATHEMATICA

RealDigits[E^(5*Pi/6) * Gamma[1/4] * (5^(1/4) - 1) * Sqrt[(Sqrt[5] - 1)/5] / (2^(19/8)*Pi^(3/4)), 10, 120][[1]]

RealDigits[QPochhammer[E^(-20*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)), 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)).

Sequence in context: A363179 A292864 A363120 * A099646 A181693 A271880

Adjacent sequences: A363018 A363019 A363020 * A363022 A363023 A363024

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, May 13 2023

STATUS

approved