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Search: id:A089801
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| A089801 |
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Expansion of Jacobi theta function (theta_3(q^(1/3))-theta_3(q^3))/2/q^(1/3). |
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+0
4
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| 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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I. J. Zucker, "Further Relations Amongst Infinite Series and Products. II. The Evaluation of Three-Dimensional Lattice Sums." J. Phys. A: Math. Gen. 23, 117-132, 1990.
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LINKS
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Eric Weisstein's World of Mathematics, Jacobi Theta Functions
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FORMULA
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Euler transform of period 12 sequence [1, -1, 0, 0, 1, -1, 1, 0, 0, -1, 1, -1, ...]. - Michael Somos, Apr 12 2005
a(n)=b(3n+1) where b(n) is multiplicative and b(3^e)=0^e, b(p^e)=(1+(-1)^e)/2 if p<>3. - Michael Somos Jun 06 2005
Expansion of q^(-1/3)*eta(q^2)^2*eta(q^3)*eta(q^12)/(eta(q)*eta(q^4)*eta(q^6)) in powers of q. - Michael Somos Apr 12 2005
Expansion of chi(q)* psi(-q^3) in powers of q where chi(), psi() are Ramanujan theta functions. - Michael Somos, Apr 19 2007
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = 2^(1/2) (t/i)^(1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A089807.
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EXAMPLE
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1 + q + q^5 + q^8 + q^16 + q^21 + q^33 + q^40 + q^56 + q^65 + q^85 + ...
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PROGRAM
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(PARI) a(n)=issquare(3*n+1) /* Michael Somos Apr 12 2005 */
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CROSSREFS
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A089802(n)=(-1)^n*a(n).
Sequence in context: A117964 A094875 A012245 this_sequence A089802 A143064 A163811
Adjacent sequences: A089798 A089799 A089800 this_sequence A089802 A089803 A089804
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Nov 12, 2003
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