Bill said, correctly:
Lotsa sequences here.
Me: I hope someone will submit them to the OEIS. I don't have time myself (see following paragraph). But there are a lot of OEIS fans on this list, I believe. Neil - Dear Friends, I will soon be retiring from AT&T. New coordinates: Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Sun, Feb 19, 2012 at 10:17 PM, Bill Gosper <billgosper@gmail.com> wrote:
VE>
How does one report bugs to Wolfram?
In:=Sum[(-1)^k Binomial[m, k] k, {k, 0, m}]
Out:=0
It gets the correct answer when m is given explicitly. I'm guessing it knows
Sum[z^k Binomial[m, k] k, {k, 0, m}]
and then chokes when it evaluates for z=-1.
Veit
As far as I'm concerned, the real bug is that it did anything at all before you typed FunctionExpand or the like.
http://www.wolfram.com/support/contact/email/ should work. They used to have support.wolfram.com/submitabug.cgi . I can send you a copy of the web page and associated files if you want to try it.
Speaking of Wolfram.com,
http://reference.wolfram.com/mathematica/ref/QPochhammer.html (Neat examples) gives "Hirschhorn's modular identity ":
In[673]:= Series[ QPochhammer[q, q]^5 - QPochhammer[q^5, q^5], {q, 0, 99}]
Out[673]= SeriesData[q, 0, {-5, 5, 10, -15, -5, -5, 25, 15, -20, 10, -45, -5, 25, 20, 10, 15, 20, -50, -35, -30, 55, -50, 15, 80, 0, 50, -35, -45, -15, 5, -50, -25, -55, 85, 50, 50, 10, -40, 65, 10, -10, -115, 50, -115, -100, 85, 80, -30, 5, 20, 45, 70, 65, 45, -55, -100, -45, 10, -115, 110, -160, 55, -20, -70, 110, -20, 105, 185, 70, -130, -85, 65, 60, -50, 0, -130, 10, -55, -165, -110, 165, 15, 55, -30, 160, 45, -60, 90, -5, 10, 100, 165, -155, 60, -230, -145, -55, -45, 35}, 1, 100, 1]
In fact this seems to hold for *all* primes:
In[716]:= Table[Collect[Series[QPochhammer[q]^p - QPochhammer[q^p], {q, 0, 999}], q, Modulus -> p], {p, Prime@Range[99]}]
Out[716]= {0, 0, 0, 0,..., 0}
For p=5, the coefficients match for a peculiar (infinite?) power sequence: In[679]:=Flatten[ Position[CoefficientList[Normal[Series[QPochhammer[q, q]^5 - QPochhammer[q^5, q^5], {q, 0, 4076}]], q], 0]]-1
Out[679]= {0, 25, 75, 175, 350, 1560, 1802, 1838, 2318, 2690, 3174, 3742, 3925}
QPochhammer[q, q]^3 = QPochhammer[q^3, q^3] *except* at q^binomial(n,2), n>1.
QPochhammer[q, q]^2 matches QPochhammer[q^2, q^2] at q powers
0, 2, 7, 10, 11, 12, 17, 18, 21, 22, 24, 25, 32, 37, 39, 41, 42, 43, 44, 46, 47, 49, 52, 54, 57, 58, 60, 62, 65, 67, 68, 70, ...
QPochhammer[q, q]^15 matches QPochhammer[q^15, q^15] at powers 0, 53, 482, 1340, ...
QPochhammer[q, q]^n appears to match QPochhammer[q^n, q^n] only at q^0 for n in {7,9,11,13,17,...}!
For n=4, the matches are 0, 9, 14, 19, 24, 31, 34, 39, 42, 44, 49, 53, 59, 64, 65, 69, 74, 75,... For n=6, 0, 5, 8, 14, 17, 19, 23, 26, 32, 33, 35, 40, 41, 44, 47, 50, 52, 53, 54 For n=8, 0, 3, 7, 11, 13, 15, 18, 19, 23, 27, 28, 29, 31, 35, 38, 39
Lotsa sequences here. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun