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| A000521
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Coefficients of modular function j as power series in q = e^(2 Pi i t). Another name is the elliptic modular invariant J(tau).
(history;
published version)
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#254 by N. J. A. Sloane at Mon Jul 01 12:53:27 EDT 2024
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#253 by N. J. A. Sloane at Mon Jul 01 12:53:25 EDT 2024
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| LINKS
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John Cremona, <a href="httphttps://www.maths.nott.ac.uk/personal/jec">Home page</a>
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approved
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#252 by Michel Marcus at Mon Feb 26 01:27:50 EST 2024
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#251 by Joerg Arndt at Mon Feb 26 01:15:16 EST 2024
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#250 by Joerg Arndt at Mon Feb 26 01:15:13 EST 2024
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#249 by Joerg Arndt at Mon Feb 26 01:15:02 EST 2024
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a[n_] := SeriesCoefficient[ 12^3 KleinInvariantJ[Log[q]/(2 Pi I)], )], {q, 0, n}] (* _Leo C. Stein_, Feb 25 2024 *)
{q, 0, n}] (* Leo C. Stein, Feb 25 2024 *)
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proposed
editing
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Discussion
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| Mon Feb 26
| 01:15
| Joerg Arndt: thanks!
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#248 by Leo C. Stein at Mon Feb 26 00:53:26 EST 2024
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#247 by Leo C. Stein at Mon Feb 26 00:49:16 EST 2024
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a[n_] := SeriesCoefficient[With[{L = InverseEllipticNomeQ[Sqrt[q]]}, rootQ]}, 256 (L^2 - L + 1)^3/(L (1 - L))^2], {qrootQ, 0, n2n}]; (* Jan Mangaldan, Jul 07 2020, after _Michael Somos_ *)_; corrected by _Leo C. Stein_, Feb 25 2024 *)
a[n_] := SeriesCoefficient[ 12^3 KleinInvariantJ[Log[q]/(2 Pi I)],
{q, 0, n}] (* Leo C. Stein, Feb 25 2024 *)
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approved
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Discussion
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| Mon Feb 26
| 00:52
| Leo C. Stein: There seems to be a Mathematica bug that made the function by Jan Mangaldan incorrect (the math itself is correct, but Mathematica gave an incorrect result starting with a(3)). This was corrected by avoiding the square root in his function. At the same time I added the most native approach I could write in Mathematica.
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#246 by N. J. A. Sloane at Mon Sep 18 13:15:21 EDT 2023
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#245 by N. J. A. Sloane at Mon Sep 18 13:15:18 EDT 2023
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| REFERENCES
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Evans, David E., and Yasuyuki Kawahigashi. "Subfactors and mathematical physics." Bulletin of the American Mathematical Society, 60:4, (2023), 459-482 (see page 472).
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approved
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