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If a function is differentiable at some point c of its domain, then it is also continuous at c. However here we extend the notion of differentiability to be valid for individual points on the real number line, specifically positive integers.

 f(n)=(-1)^n* n^(1/n)

THEOREM MRBK 8.0

f=f' / (I*Pi+(1-ln(n))/n^2)| n ∈ {1,2,3,...}

By THEOREM MRBK 4.0, When n is in the set of (positive) integers the derivative of f is exactly I*Pi*f+(1-ln(n))*f/n^2.

So f' = I*Pi*f+(1-ln(n))*f/n^2| n ∈ {1,2,3,...}

Solving for f, we have the following:

f' = I*Pi*f+(1-ln(n))*f/n^2

f' = f*(I*Pi+(1-ln(n))/n^2)

f=f' / (I*Pi+(1-ln(n))/n^2)

 

For more on this click here (W/A).

how can i found the integer number after any divident using maple commands

like

(13/4)

 

Am I missing some justification for this last one?

> zip(`/`,Array([3]),Array([9]));
                                     [1/3]
 
> zip(`/`,Array([3],datatype=integer[4]),Array([9]));
                                     [1/3]
 
> zip(`/`,Array([3]),Array([9],datatype=integer[4]));
                                     [1/3]
 
> zip(`/`,Array([3],datatype=integer[4]),Array([9],datatype=integer[4]));
                            [0.333333333333333315]

In the list of how irrational, rational, and from small to large integers to sort.Can not calculate irrational. Can you help? Thanks

Since the MRB constant is an alternating sum of positive integers to their own roots, f(n)=(-1)^n* n^(1/n); a thorough understanding of the changes in f, as n changes, is important.
In this blog we will begin to explore the derivative of f at integer values of n, and as n-> infinity. I am not sure weather this will help us in computing more digits of the MRB constant since we already know so many,

okay, so I was asked this question

Hello Everyone,

 

i try to solve a function for zero (numerically) that contains the cdf of the binomial distribution, but i can't get i work. Maple (13) simply returns the equation without any solution.... Or strikes because of the non-algebraic content...

 

Let p(x,t) describe a probability for a binary event. Let Bcdf(z-2,n,p(x,t)) denote the binomial cdf such that the probability that this event happens at least z  out of n times, where z and n  are integers.

I want to compute:

I did the following:

 

restart;
with(Statistics):
CRRA := t->((t)^(1-rho))/(1-rho);
X1 := RandomVariable(Geometric(q));
assume(t::integer, 0 < rho, rho <> 1, 0 < q, q < 1);
ExpectedValue(CRRA(X1));

As result I get a formula, where Maple defines _t0 (as far as I can see in italic font).

But why does Maple do so, and what does this mean?

 

Thx for answering.
 

I want to evaluate a polynomial and turn its coefficients into hfloats. Shouldn't evalhf do this? For example:
f := randpoly([x,y,z]);  # integer coefficients
g := evalf(f);    # software float coefficients
h := evalhf(f);   # error
I think the last one should give me a polynomial with hardware floating point coefficients. Instead I get an error.

I have a multivariable function, F(n, g(1,0),g(0,1),g(0,2),g(1,1),g(2,1),...,g(n,1),g(n-1,2),...,g(1,n)), of indeterminates g(i,j) (omitting g(0,0) - in other words - let L = set of all pairs of nonnegative integers, (i,j), which satsify 1<= i+j <=n) of the following form F = product over all the (i,j) in L of g(i,j)^h(i,j) / ((i!

hi, suppose

integers:=[`$`(-10..10)]; selectremove(`<`,integers,0);

so this separates +ve and -ve. But, if the range of values are complex, how do we separate them based on the +ve and -ve of the real part of the complex number? i.e I want to separate all a +- bi from all -a +- bi.

 

thanks

Hi all,

 

I am after some advice on how to extract a value from a proc.

 

f := (k-1)^(p-1)/k; p := 1.99; maximize(f, k = 2 .. infinity, location); this is the problem... and it's working fine... but.. how do i make k take on only integer values?

I have only found rand() which gives me integer values and I need to generate (a lot of)  random rational numbers.

The boundary (0,2) doesn't really matter but I do need the numbers to at least go up to 2. Else any rational will do.

Thankyou.

Situation:  I have multiple lists of the form [i$i=1..n,0$k] , where n is a positive integer and k is a nonegative integer.

 

Desired result:  For each list, produce a list of permutations of the list (as you would receive from combinat[permute]) such that in each permutation, the nonnegative integers in the list appear in ascending order from left to right and no two nonnegative integers are adjacent to one another. 

 

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