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A275632
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Andrews's 4-shadow function THETA.BAR_3(q).
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2
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1, 2, 4, 6, 10, 8, 16, 12, 20, 18, 24, 16, 38, 20, 32, 32, 42, 24, 52, 28, 56, 44, 48, 32, 80, 42, 56, 54, 76, 40, 96, 44, 84, 64, 72, 64, 122, 52, 80, 76, 120, 56, 128, 60, 112, 104, 96, 64, 166, 78, 124, 96, 132, 72, 160, 96
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OFFSET
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0,2
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LINKS
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FORMULA
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See Section 1 of Andrews (2016) or the Maple code below.
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MAPLE
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F:=(a, q, n)->mul(1-a*q^i, i=0..n-1); # This is (a; q)_n
M:=15;
THETA3:=(add((-1)^n*q^(3*n^2), n=-M..M)) /(add((-1)^n*q^(n^2), n=-M..M));
s1:=series(THETA3, q, 80); seriestolist(%);
THETABAR3:=1+2*add( (F(q, q, n-1)*q^(n^2)) / (F(q^n, q, n)*(1-q^n)), n=1..M);
s2:=series(THETABAR3, q, 80); seriestolist(%);
series((s1-s2)/8, q, 80); seriestolist(%);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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