## 792 Reputation

9 years, 288 days

## Probably just mathematical entertainment...

Maple

I recently watched a video in which the speaker asked the following question: "How many seconds are there in 42 days?".
I think I've done what anyone would do: trying to quickly find an order of magnitude for this number.
But the speaker's answer was both remarkable and obvious when you think of it: "Exactly 10! seconds".

So my question: Given the number 3628800, is there a way to identify it (in the  identify's sense) to 10!  ?
Or maybe some trick to force identify to answer 10! ?

## How is binomial(n, n+p) computed when p ...

Maple

While answering a question on this site I accidentally met expressions of the form binomial(n, min(n, r)+1) where both n and r are positive integers and n is strictly lower than r.

For the record the common definition of the binomial coefficient binomial(n, k) is based on the double inequality 0 <= k <= n  and the only generalized definition where k could be larger than n I know of is the NegativeBinomial distribution where we use
binomial(-n, k) which, with 0 <= k <= n  again makes the first operator lower than the second.

I tried to understand how Maple does this

```binomial(n, min(n, r)+1) assuming n < r,  n::posint
0
```

(more generallyn, for any strictly positive integer p, binomial(n, min(n, r)+p) = 0 under the assumptions above)

I guess that the explanationrelies upon what I did to get the output (2) in the attached file.
Can you confirm/infirm this and, as I wasn't capable to find any clue in help(binomial), [Maple 2015], if the way maple computes
these results is documented elsewhere.

 > restart:

 > t0 := binomial(n, min(n, r)+1); eval(t0) assuming n < r; eval(%) assuming n::posint; # I didn't find in help(binomial) the argument used to get this last result.
 (1)
 > # What happens if binomial is converted into factorials t1 := convert(t0, factorial); eval(t1) assuming n < r;
 > # Or into GAMMA function? t2 := convert(t1, GAMMA); eval(t2) assuming n < r;
 > # Try to replace min(n, r) = n by n-epsilon and take the limit as epsilon goes to 0 # from the right. t3 := algsubs(min(n, r) = n-epsilon, t2); limit(t3, epsilon=0, right)
 (2)

We recover here the result (1), but does Maple really proceed this way?

## Why is the output of printf delayed?...

Maple 2015

When there are print commands in a loop their content is printed as soon as this command is executed.
This is not the case with printf whose displays are delayed (buffered?).
Is there a way to force the display of printf when the command is executed?

TIA

Motivation: I want to display intermediate execution times in a prettier way than print offers.

## Can we increase the presision of the sli...

Maple 2015

Is it possible to enlarge the sliders in Explore(plot(...), ...) and increase their "resolution" (meaning to have a higher precision when the slider is moved)?
If Maple does offer this option, could you tell me from what version this is the case

TIA

## How can we prove this equality?...

Maple

I'm stucked in trying to prove that rel(n)  is true for each integer n > 1.

 > restart
 > rel := n -> (n-3)^(n/(n-1))*2^(n/(n-1))-((n-1)*2^(n/(n-1))-4*2^(1/(n-1)))*(n-3)^(1/(n-1)) = 0
 (1)
 >