Re: Euler and 3

In article
<ab2793f0-7934-469a-b96b-016240a9caf9@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Mariano Suárez-Alvarez" <mariano.suarezalvarez@xxxxxxxxx> wrote:

On Jan 22, 8:44 pm, Gerry Myerson <ge...@xxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
In article <220120080930154901%ed...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"G. A. Edgar" <ed...@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

In article
<16136681.1201011521204.JavaMail.jaka...@xxxxxxxxxxxxxxxxxxxxxx>, G.E.
Ivey <george.i...@xxxxxxxxxxxxx> wrote:

The Euler-Mascheroni constant is not algebraic.

Wow. A new discovery. First announced in sci.math ... !!! ???

G. E. Ivey may not be able to prove that gamma is transcendental
but is not really going out on a limb to assert it.

Anyway, back to the question that started this thread, I suppose
one way to make sense of it is to ask whether there is some series
like gamma^2 = (1 / 3) + (1 / 3333) + (1 / 3333333) + ....
that is, some series sum (1 / a_n) where a_1 = 3 and a_n is big
for n > 1 and a_n follows some simple pattern. If there is such
a series, it might be taken as an "explanation" of the closeness
of gamma^2 and 1/3.

1/3 is the first convergent in the continued fraction development
of gamma^2.

Yes, but, do the other convergents show any pattern?

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

Relevant Pages

  • Re: Euler and 3
    ... On Jan 22, 10:52 pm, Gerry Myerson ... but is not really going out on a limb to assert it. ... Yes, but, do the other convergents show any pattern? ...
    (sci.math)
  • Re: 555 timer internal SR flipflop
    ... A 555 timer has an internal SR flipflop according to the data sheets, ... and it appears that I can feed the SR FF any 0/1 pattern I choose by picking the appropriate voltages for the pins of the 555. ... Does the "don't assert S and R at the same time" rule still ...
    (sci.electronics.design)
  • Re: Euler and 3
    ... but is not really going out on a limb to assert it. ... Yes, but, do the other convergents show any pattern? ... Gerry Myerson ...
    (sci.math)