[math-fun] Fairly concise R-R CF in theta constants
Arcsinh of (the same) four thetas, twice. http://gosper.org/R-R CF.pdf Anyone have a shorter expression? Can anyone convince Mma to Series the rhs? --rwg
The second identity should be Th2(0,sqrt(q)) * Th3(0,sqrt(q)) == 2 * eta(q)^4 / eta(sqrt(q))^2 (note squared denominator in rhs.) * Bill Gosper <billgosper@gmail.com> [Jun 21. 2010 11:29]:
Arcsinh of (the same) four thetas, twice. http://gosper.org/R-R CF.pdf Anyone have a shorter expression? Can anyone convince Mma to Series the rhs? --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Here's a fix and an elaboration: http://gosper.org/quinttheta.pdf Caution, Mathematica's DedekindEta wants argument tau, not q=exp(2 i pi tau). It really needs both flavors of eta. On Sun, Jun 20, 2010 at 8:24 PM, Bill Gosper <billgosper@gmail.com> wrote:
Arcsinh of (the same) four thetas, twice. http://gosper.org/R-R CF.pdf Anyone have a shorter expression? Can anyone convince Mma to Series the rhs? --rwg
The following may lead to more concise expressions: Th2(q)*Th3(q) == 1/2*Th2(sqrt(q)) and exp(asinh(x)) == x + sqrt(1+x^2) * Bill Gosper <billgosper@gmail.com> [Jun 24. 2010 13:18]:
Here's a fix and an elaboration: http://gosper.org/quinttheta.pdf Caution, Mathematica's DedekindEta wants argument tau, not q=exp(2 i pi tau). It really needs both flavors of eta. On Sun, Jun 20, 2010 at 8:24 PM, Bill Gosper <billgosper@gmail.com> wrote:
Arcsinh of (the same) four thetas, twice. http://gosper.org/R-R CF.pdf Anyone have a shorter expression? Can anyone convince Mma to Series the rhs? --rwg
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Bill Gosper -
Joerg Arndt