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