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A259151 Decimal expansion of phi(exp(-8*Pi)), where phi(q) = Product_{n>=1} (1-q^n) is the Euler modular function. 12
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 7, 8, 3, 8, 4, 4, 3, 2, 9, 0, 4, 4, 2, 7, 8, 8, 1, 4, 0, 9, 9, 8, 2, 7, 0, 9, 5, 9, 4, 8, 6, 9, 4, 5, 6, 7, 3, 8, 5, 2, 1, 9, 8, 5, 4, 3, 8, 7, 2, 7, 2, 5, 5, 8, 3, 6, 9, 9, 1, 5, 5, 2, 6, 6, 6, 2, 6, 9, 2, 7, 0, 0, 5, 5, 6, 6, 7, 5, 0, 6, 5, 2, 1, 7, 6, 4, 9, 3, 2, 7, 9, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..102.

Istvan Mezo, Several special values of Jacobi theta functions arXiv:1106.2703v3 [math.CA] 24 Sep 2013

Eric Weisstein's MathWorld, Infinite Product

Eric Weisstein's MathWorld, Jacobi Theta Functions

Eric Weisstein's MathWorld, q-Pochhammer Symbol

Wikipedia, Euler function

FORMULA

phi(q) = QPochhammer(q,q) = (q;q)_infinity.

phi(q) also equals theta'(1, 0, sqrt(q))^(1/3)/(2^(1/3)*q^(1/24)), where theta' is the derivative of the elliptic theta function theta(a,u,q) w.r.t. u.

phi(exp(-8*Pi)) = (sqrt(2) - 1)^(1/4)*exp(Pi/3)*(Gamma(1/4)/(2^(29/16)*Pi^(3/4))).

A259151 = A259147 * exp(5*Pi/16)/2. - Vaclav Kotesovec, Jul 03 2017

EXAMPLE

0.999999999987838443290442788140998270959486945673852198543872725583699...

MATHEMATICA

phi[q_] := QPochhammer[q, q]; RealDigits[phi[Exp[-8*Pi]], 10, 103] // First

CROSSREFS

Cf. A048651 phi(1/2), A100220 phi(1/3), A100221 phi(1/4), A100222 phi(1/5), A132034 phi(1/6), A132035 phi(1/7), A132036 phi(1/8), A132037 phi(1/9), A132038 phi(1/10), A292862 phi(exp(-Pi/8)), A292863 phi(exp(-Pi/4)), A259147 phi(exp(-Pi/2)), A259148 phi(exp(-Pi)), A259149 phi(exp(-2*Pi)), A292888 phi(exp(-3*Pi)), A259150 phi(exp(-4*Pi)), A292905 phi(exp(-5*Pi)), A292864 phi(exp(-16*Pi)).

Sequence in context: A292905 A269351 A116667 * A270172 A137577 A292864

Adjacent sequences:  A259148 A259149 A259150 * A259152 A259153 A259154

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Jun 19 2015

STATUS

approved

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Last modified February 19 22:36 EST 2020. Contains 332061 sequences. (Running on oeis4.)