BG> By uncontrived I meant not explicitly constructed as a continued fraction. Just my two cents: http://ttk.pte.hu/mii/html/pannonica/index_elemei/mp17-1/mp17-1-091-110.pdf claims that (1;2,4,8,16...) is equal to 1+Sum[1/((-1)^n*2^(1 + n)^2*QPochhammer[4, 4, n]), {n, 0, Infinity}]/ Sum[1/((-1)^n*2^n^2*QPochhammer[4, 4, n]), {n, 0, Infinity}] (The source, Takao Komatsu's "Hurwitz and Tasoev Continued Fractions with Long Period" cites another paper, "On Hurwitzian and Tasoev's Continued Fractions", by the same author, but which I can't seem to find) --Neil Bickford On Thu, Sep 27, 2012 at 10:33 AM, Allan Wechsler <acwacw@gmail.com> wrote:
If x is Hurwitz then so is x/2, so, uh ...
I think that by "contrived" Gosper means "with cf terms explicitly chosen to be non-periodic". An example would be (1;2,4,8,16...). I'm assuming that there is not a single such example that anybody knows a "closed form" for; the closed form thereof would answer Gosper's query.
On Thu, Sep 27, 2012 at 12:54 PM, meekerdb <meekerdb@verizon.net> wrote:
Is the smallest contrived Hurwitz, thereby uncontrived? :-)
Brent
On 9/27/2012 5:38 AM, Bill Gosper wrote:
Can someone name a single (uncontrived) constant (e.g., π, e^3, 2^(1/3), parity number,...) that is provably nonHurwitz? And if Hurwitz, is not homographically equivalent to a single- mover, linear?
Boy, are we ignorant. --rwg ______________________________**_________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
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