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#11 by Charles R Greathouse IV at Fri Mar 12 22:24:46 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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#10 by N. J. A. Sloane at Wed Nov 13 21:58:48 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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#9 by Joerg Arndt at Thu Aug 10 03:18:57 EDT 2017
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#8 by G. C. Greubel at Thu Aug 10 02:58:06 EDT 2017
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#7 by G. C. Greubel at Thu Aug 10 02:57:58 EDT 2017
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a[ n_] := SeriesCoefficient[ ([(QPochhammer[-q, q^2]/(QPochhammer[ -x[-q^3, xq^3]^3 / QPochhammer[ -x, x6])^3)^2, {xq, 0, n}]; (* Michael Somos, Sep 02 2015 *)(* Corrected by G. C. Greubel_, Aug 10 2017 *)
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#6 by G. C. Greubel at Thu Aug 10 02:56:52 EDT 2017
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G. C. Greubel, <a href="/A164614/b164614.txt">Table of n, a(n) for n = 0..1000</a>
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| STATUS
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approved
editing
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#5 by Michael Somos at Wed Sep 02 12:05:22 EDT 2015
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#4 by Michael Somos at Wed Sep 02 12:05:01 EDT 2015
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Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A010054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
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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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q^2G.f. = 1 + 2*q^5x + qx^82 - 4*qx^113 - 8*qx^144 - 2*qx^175 + 14*qx^206 + 24*x^7 + 6*qx^238 + ...
G.f. = q^2 + 2*q^5 + q^8 - 4*q^11 - 8*q^14 - 2*q^17 + 14*q^20 + 24*q^23 + ...
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a[ n_] := SeriesCoefficient[ (QPochhammer[ -x^3, x^3]^3 / QPochhammer[ -x, x])^2, {x, 0, n}]; (* Michael Somos, Sep 02 2015 *)
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(PARI) {a(n) = localmy(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^12 + A)^3 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^6))^2, n))}))};
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Cf. A128111.
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approved
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Discussion
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| Wed Sep 02
| 12:05
| Michael Somos: Added more info. Light edits. Revised Ramanujan theta comment. Updated URL.
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#3 by Charles R Greathouse IV at Thu Mar 05 13:24:05 EST 2015
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Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054A010054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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Discussion
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| Thu Mar 05
| 13:24
| OEIS Server: https://oeis.org/edit/global/2357
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#2 by Charles R Greathouse IV at Wed Apr 30 01:37:14 EDT 2014
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| AUTHOR
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_Michael Somos, _, Aug 17 2009
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Discussion
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| Wed Apr 30
| 01:37
| OEIS Server: https://oeis.org/edit/global/2182
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