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Re: different results

• To: mathgroup at smc.vnet.net
• Subject: [mg125324] Re: different results
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Tue, 6 Mar 2012 06:01:14 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201203050742.CAA29927@smc.vnet.net>

f[x_] = Product[1 + x^(8*i - 1), {i, 1, Infinity}];
g[x_] = Product[(1 - x^(8*i - 1)), {i, 1, Infinity}];
h[x_] = (1 + 2*f[x])/(-1 + g[x]);

Series[h[x], {x, 0, 10}] // Normal

-2 - 3/x^7 + 3*x - 3*x^8

The "first" coefficient for h[x] is for the x^-7 term. If you want all
of the coefficients you need to look at x^7*h[x]

CoefficientList[Series[x^7*h[x], {x, 0, 107}], x]

{-3, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -4, 3, \
0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, -4, 2, 3, 0, 0, 0, 0, 0, -3, -9, -3, \
0, 0, 0, 0, -4, 1, 5, 3, 0, 0, 0, 0, 1, -15, -9, -3, 0, 0, 0, -4, 0, 6, 5, 3, \
0, 0, 0, 5, -20, -21, -12, -3, 0, 0, -4, -1, 16, 11, 11, 3, 0, 0, 9, -20, \
-40, -36, -18, -3, 0, -4, -6, 31, 27, 25, 14, 3, 0, 13, -15, -61}


Bob Hanlon


On Mon, Mar 5, 2012 at 2:42 AM, Roger Bagula <roger.bagula at gmail.com> wrote:
> Two versions of the code:
> Table[SeriesCoefficient[
> Series[(1 + 2*Product[1 + x^(8*i - 1), {i, 1, Infinity}])/(-1 +
>  Product[(1 - x^(8*i - 1)), {i, 1, Infinity}]), {x, 0, 100}],
> n], {n, 0, 100}]
>
> f[x_] = Product[1 + x^(8*i - 1), {i, 1, Infinity}]
> g[x_] = Product[(1 - x^(8*i - 1)), {i, 1, Infinity}]
> h[x_] = (1 + 2*f[x])/(-1 + g[x])
> a = Table[SeriesCoefficient[
>   Series[h[x], {x, 0, 100}], n], {n, 0, 100}]
>
> Discussion at:https://oeis.org/draft/A208150
> I get as I submitted:
> DATA    -2, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -4, 3, 0, 0, 0,
> 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, -4, 2, 3, 0, 0, 0, 0, 0, -3, -9, -3,
> 0, 0, 0, 0, -4, 1, 5, 3, 0, 0, 0, 0, 1, -15, -9, -3, 0, 0, 0, -4, 0,
> 6, 5, 3, 0, 0
>
> An OEIS editor gets:
> [-3, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0,
> -4, 3, 0, 0, 0, ...]
> Roger Bagula
>

• References:
  • different results
    • From: Roger Bagula <roger.bagula@gmail.com>