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| A233670
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Expansion of q * phi(-q^2) * psi(q^9) / (f(q^3) * phi(q^3)) in powers of q where f(), phi(), psi() are Ramanujan theta functions.
(history;
published version)
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#13 by Charles R Greathouse IV at Fri Mar 12 22:24:47 EST 2021
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M. Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
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Discussion
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| Fri Mar 12
| 22:24
| OEIS Server: https://oeis.org/edit/global/2897
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#12 by N. J. A. Sloane at Wed Nov 13 21:58:50 EST 2019
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M. Somos, <a href="http://somos.crg4.com="/A010815/multiqa010815.htmltxt">Introduction to Ramanujan theta functions</a>
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Discussion
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| Wed Nov 13
| 21:58
| OEIS Server: https://oeis.org/edit/global/2832
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#11 by Wesley Ivan Hurt at Mon Oct 09 21:59:41 EDT 2017
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#10 by Wesley Ivan Hurt at Mon Oct 09 21:58:59 EDT 2017
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| MATHEMATICA
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A233670[n_] := SeriesCoefficient[q*QPochhammer[q^2]^2*QPochhammer[q^3]^3 *QPochhammer[q^12]^3*QPochhammer[q^18]^2/(QPochhammer[q^4] * QPochhammer[q^6]^8*QPochhammer[q^9]), {q, 0, n}]; Table[A233670[n], {n, 0, 50}] (* G. C. Greubel, Oct 09 2017 *)
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reviewed
editing
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#9 by Joerg Arndt at Mon Oct 09 02:47:35 EDT 2017
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#8 by G. C. Greubel at Mon Oct 09 02:45:16 EDT 2017
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#7 by G. C. Greubel at Mon Oct 09 02:45:08 EDT 2017
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G. C. Greubel, <a href="/A233670/b233670.txt">Table of n, a(n) for n = 1..1000</a>
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| MATHEMATICA
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A233670[n_] := SeriesCoefficient[q*QPochhammer[q^2]^2*QPochhammer[q^3]^3 *QPochhammer[q^12]^3*QPochhammer[q^18]^2/(QPochhammer[q^4] * QPochhammer[q^6]^8*QPochhammer[q^9]), {q, 0, n}]; Table[A233670[n], {n, 0, 50}] (* G. C. Greubel, Oct 09 2017 *)
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| STATUS
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approved
editing
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#6 by Michael Somos at Thu Aug 27 00:12:38 EDT 2015
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#5 by Michael Somos at Thu Aug 27 00:12:16 EDT 2015
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| LINKS
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M. Somos, <a href="http://cissomos.csuohiocrg4.edu/~somoscom/multiq.pdfhtml">Introduction to Ramanujan theta functions</a>
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| FORMULA
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G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = f(t) where q = exp(2 piPi i t).
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| PROG
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(PARI) {a(n) = localmy(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^12 + A)^3 * eta(x^18 + A)^2 / (eta(x^4 + A) * eta(x^6 + A)^8 * eta(x^9 + A)), n))}))};
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| STATUS
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approved
editing
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Discussion
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| Thu Aug 27
| 00:12
| Michael Somos: Light and space edits. Updated URL.
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#4 by Joerg Arndt at Sat Dec 14 13:14:01 EST 2013
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