Factorial/Exponential Identity, Infinity 2015

[Ross A. Finlayson]

Factorial/Exponential Identity, Infinity 2015


"The number looked a bit like sqrt{8/pi}." -- R. Carr
Also, 2 sqrt{2/pi}.

":Here I plan to return the variable x to n/2.
:
:f(n) = gamma( n/2 + 3/2) / ( sqrt(n/2) gamma(n/2)^2 2^(2n-4) )
:
:I'm not sure if that's right, I just wrote it right now and haven't
:reviewed it many times.
:
:Please explain your reasoning and thought process about this.
:
:I'm thinking here that lim n->oo f(n) = sqrt(8/Pi)"

"Do you have a proof of this identity? "

(RF on the fact.)


"I actually used Stirling,
I'm afraid to sandwich the limit
between sqrt{8/pi}-g(n) and sqrt{8/pi}+h(n)
where g(n),h(n)->0 as n->infinity (at least [f]or
even n)." -- R. Carr

Ha, "I actually used Stirling".

Then, there is the error term it is the residual.
That's for subtracting that out from the floor,
or Hadamard etc under what square the now
the constant replacement of 2 sqrt{2/pi} here is.

Or, maybe it is variously not under that
(the square floor here of the form).


These are more forms for Stirling!

Listen to me bragging!

So, here, I am to explain to you
that this is for the first step canonical form,
(second) only itself and that is so far, for what
extension of what these "constants" or "invariants"
here are.

This one for example is of the canonical sequence
notice of the 2's, then for 3's and so on. Themselves
these are just values in the refinements of the numerical
approximation of as above a value as established via space concerns.

This identity of sorts is discovered as simply going through those,
where it is of a family of identities that they are. Similar for example
are Bernoulli principles. Here, as an identity then it is also useful with
setting to equal 1, and maintaining cancellation of algebra with the neat
and parameterized term!

space concerns

Stirling and cycles

Gamma

Hadamard, Hadamard/Euler

factorial, n!

Pochhammer etc as notation

Then, for numerical methods as also having an
approximating result when computed, it is relevant
for usual maintenance of the term that the error term
of the approximation is maintained. Then, for above,
the comment is that it's at least reasonable enough to
begin its maintenance then as to then for bounds or
suitability in a framework of numerical methods for
effectively correct results.

This is the highest mountain of these numbers in the
series that it begins I know!

The terms are always reducing redundantly!

There are various results and lines of results.

This "space concerns" consideration is not entirely
unreasonable - space concerns of the space of the
sequences of the value space, and, the expectation
space (probabilistic space concerns as they usually are,
here of these forms as parameterizing value space).

I didn't invent this so much as find it, after already
establishing the space concern (which establishes itself).

[abu.ku...@gmail.com]

what a load of

[Ross A. Finlayson]

It's exquisite!

They already have this, I am figuring out
what it is to put together. ("They" being
"mathematics and physics".) I mostly studied
mathematics and physics in school, then there
is "to learn".

The constructivist enjoys this!