OEIS could probably use more such asymptotic formulæ.
Yes, please! I try to add them wherever I can, but there are nearly a quarter-million sequences, the majority of which have no asymptotic formulae at all. Charles Greathouse Analyst/Programmer Case Western Reserve University On Tue, Mar 11, 2014 at 1:03 PM, Bill Gosper <billgosper@gmail.com> wrote:
Besides Warren's proposals, Dodgson's method is valuable theoretically, helping Rich prove my Somos addition formulæ http://arxiv.org/abs/math/0703470 and Zeilberger prove the famously challenging Alternating Sign Matrix Theorem (A005130), the "Stirling's formula" for which is
Out[264]= (2^(5/12 - 2*n^2)*3^(-(7/36) + (3*n^2)/2)* E^((1/3)*HoldForm[Derivative[1][Zeta][-1]])*Pi^(1/3))/ (n^(5/36)*Gamma[1/3]^(2/3))
(the HoldForm to fend off that vexatious Glaisher symbol).
In[265]:= Table[N[ReleaseHold[%]], {n, 9}] // InputForm
Out[265]//InputForm= {1.0063254118710128, 2.003523267231662, 7.0056223910285915, 42.01915917750558, 429.12582410098327, 7437.518404899576, 218380.8077275304, 1.085146545456063*^7, 9.119184824937415*^8}
the actual sequence being
1, 1, 2, 7, 42, 429, 7436, 218348, 10850216, 911835460, 129534272700,
Adamchik may have already worked this out someplace, in spite of the painful obstacles thrown up by Mathematica.
OEIS could probably use more such asymptotic formulæ. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun