More generally, [$]f(x) = \pi^x[$] satisfies the ODE

[$]df/dx = a f, f(0) = 1[$] where [$]a = log(\pi)[$].

I would solve in multiprecision in NDSolve, may better than raw multiplication.

Is [$]\pi^e < e^\pi[$], what?

Statistics: Posted by Cuchulainn — November 9th, 2017, 9:12 am

]]>

Cuchulainn: "Physicists have bouts of anxiety. "

it is known as the Heisenberg’s uncertainty principle. I am sure it has an upper limit. so you can stop being so anxious that your electrons could be outside the visible universe at this moment in time.

Statistics: Posted by Traden4Alpha — November 8th, 2017, 1:30 am

]]>

it is known as the Heisenberg’s uncertainty principle. I am sure it has an upper limit. so you can stop being so anxious that your electrons could be outside the visible universe at this moment in time.

Statistics: Posted by Collector — November 7th, 2017, 11:16 pm

]]>

The physicist says: "The universe is a model of my equations."

The mathematician says: "I don't care."

Physicists have bouts of anxiety.

Statistics: Posted by Cuchulainn — November 7th, 2017, 10:45 pm

]]>

This corresponds to a rapidity of w=5, that again correspond to a quite high relativistic doppler shift and a velocity ratio of

\(v/c=\tanh(5)\approx \) c x 0.999909204/c

someone would possibly call this a Pseudorapidity , but that is something different Pseudorapidity

in my max velocity theory: for rest-mass particles with this as max rapidity correspond to a hypothetical particle with reduced Compton wavelength of \(\bar{\lambda}=\frac{1}{2}e^5l_p\)

anyway I leave \(e^5\) to people doing sinful usury and mathematicians "that only are dealing with the structure of the reasoning...that don't even need to know what they are talking about...or what they they say is true.."

Statistics: Posted by Collector — November 7th, 2017, 10:22 pm

]]>

\(\pi^5\) more interesting ?

"good" old speculative numerology:

Start a pi^5 thread.

http://www.espenhaug.com/BlackHoleHedgeFund.html

Statistics: Posted by Cuchulainn — November 7th, 2017, 9:59 pm

]]>

]]>

"good" old speculative numerology:

Statistics: Posted by Collector — November 7th, 2017, 8:01 pm

]]>

Cuchulainn wrote:* An opportunity forinterval arithmetists

[$] (1 + 1/x)^{x} < e < (1 + 1/x)^{x+1}, x > 0.[$]

1, Show it is unique

2. Find an algorithm to bracket e to 0.01 accuracy.

Or one can go straight for a solution to the OP's question:

[$] (1 + 1/x)^{5*x} < e^{5} < (1 + 1/x)^{5*x+5}, x > 0.[$]

That would be the corollary, indeed. The function is monotone, so we are in luck.

And tight bounds is the 148 million dollar question. How to compute, Will Smith.

Statistics: Posted by Cuchulainn — November 6th, 2017, 2:00 pm

]]>

* An opportunity for

[$] (1 + 1/x)^{x} < e < (1 + 1/x)^{x+1}, x > 0.[$]

1, Show it is unique

2. Find an algorithm to bracket e to 0.01 accuracy.

Or one can go straight for a solution to the OP's question:

[$] (1 + 1/x)^{5*x} < e^{5} < (1 + 1/x)^{5*x+5}, x > 0.[$]

Statistics: Posted by Traden4Alpha — November 6th, 2017, 12:41 pm

]]>

[$]1/e == \displaystyle\lim_{n\to\infty} (1 - 1/n)^{n} [$].

Statistics: Posted by Cuchulainn — November 6th, 2017, 10:56 am

]]>

[$] (1 + 1/x)^{x} < e < (1 + 1/x)^{x+1}, x > 0.[$]

1, Show it is unique

2. Find an algorithm to bracket e to 0.01 accuracy.

Statistics: Posted by Cuchulainn — November 6th, 2017, 10:47 am

]]>

Big [$]e^5[$]ndians and little [$]e^5[$]ndians, what?

right on!

Statistics: Posted by Collector — November 5th, 2017, 10:38 pm

]]>

Big [$]e^5[$]ndians and little [$]e^5[$]ndians, what?

Statistics: Posted by Cuchulainn — November 5th, 2017, 10:00 pm

]]>

So, yer standard optimisers are a load of junk, we use differential evolution witth a population of 1000 and 1000 generations to give 0.3678944 80131139.

Statistics: Posted by Cuchulainn — November 5th, 2017, 9:01 pm

]]>