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These are questions asked by sand15

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! ?

Thanks in advance

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

(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.

Thanks in advence.



Let us start with this result


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.

binomial(n, min(n, r)+1)


binomial(n, n+1)




# What happens if binomial is converted into factorials

t1 := convert(t0, factorial);
eval(t1) assuming n < r;

factorial(n)/(factorial(min(n, r)+1)*factorial(n-min(n, r)-1))


Error, (in assuming) when calling '`one of {eval, min, factorial}`'. Received: 'numeric exception: division by zero'


# Or into GAMMA function?

t2 := convert(t1, GAMMA);
eval(t2) assuming n < r;

GAMMA(n+1)/(GAMMA(min(n, r)+2)*GAMMA(n-min(n, r)))


Error, (in assuming) when calling 'GAMMA'. Received: 'numeric exception: division by zero'


# 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)






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


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?


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

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


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


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

proc (n) options operator, arrow; (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 end proc




Do you have any idea to do this?


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