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I have the following expression.

 

What I want to do is take the derivative of this expression with respect to,

 

Where L is somewhere between 1 and n. 

Using the diff operator, I would like to get something like,

 

But I don't.  Instead, I get zero.  I want to leave n undefined so that the summation isn't automatically expanded out to alot of terms, thereby making it much more difficult to read.  This is especially true as my formulas become more complicated.

 

Thanks!!

 

Dear all;

 

Hello everybody, I need your help to dispaly some values obtained using my function f. When I run the code there is no results obtained. Many thanks.

restart:

# The vectors e(i) satify the folowing conditions
e(0)*e(1)=e(n-1) assuming  1<n;
e(0)*e(0)=e(2):
e(1)*e(1)=e(n-1) assuming  1<n: :
e(2)*e(1)=e(n) assuming  1<n:
#
for i from 1  to n-1 do
e(i)*e(0)=e(i+1);
end do:

# We define the function f
f:=e(0)->e(0)+(n-3)*e(1);
f:=e(1)->(n-2)*e(1);
for i from 2  to 3 do
f:=e(i)->(n+i-3)*e(i)+(i-1)*(n-3)*e(n-3+i);
end do:

for i from 4 to n do
f:=e(i)->(n+i-3)*e(i)
end do:

# We define the two vectors
x:=sum(alpha(k)*e(k),k=0..n);
y:=sum(beta(k)*e(k),k=0..n);

#Question : I would like to compute the following  but there is no display of the solution. 
(x*y);
f(x*y);
f(x);
f(y);
x*f(y);
f(x)*y;
f(x*y)- f(x)*y-x*f(y);

Hello,

I have a vector with 4 components. Each component is a polynom.

N := Vector[row](4, {(1) = -(1/2)*t^3+t^2-(1/2)*t, (2) = (3/2)*t^3-(5/2)*t^2+1, (3) = -(3/2)*t^3+2*t^2+(1/2)*t, (4) = (1/2)*t^3-(1/2)*t^2});
N[1]+N[2]+N[3]+N[4];
sum(N[i], i = 1..4);

I don't why the function sum doesn't work in this case. If i do the sum like this N[1]+N[2]+N[3]+N[4];, it works but it doesn't work with the use of the sum function.

Thank you for your help.

Good evening,

I am trying to solve the following sum equation:

 

sum((factorial(n)/factorial(2*n))^n, n = 1 .. infinity)

 

but I require the step-by-step solution as to how it is done, but can't seem to find that option. 

 

If anone could help me out, that would be great.

 

Kind regards,

A

 

Cn ={ 1, n = 0 ,                                                  }

      {Xn−1[sum of] k=0   C(k)C(n−1−k) , otherwise.  }

 

looking to complete the definition of catalan so that catalan(n) returns Cn whenever n is a non-negative integer. usin g the definition above...any help appreciated

 

catalan:=
proc(n::TYPE)
description "Print the n'th Catalan number.";
option remember;
---MORE STUFF HERE---
end proc; # catalan

I'm begginer and I don't know, whether this equation can be solved in Maple:

equation

The only variable is N.

i=1,2,3,...,n

n=the nearest smaller natural number from the second expression.

The equation sides probably won't be equal precisely, also I'm looking for some N when equation side's values are close enough.

Can you help me with programming this into Maple?

If I do even expansion for the function 2*x-2, x from [0,1], to the real line,how do I make Maple to produce

the Fourier cosine expansion in the form 2*x-2=a_0/2+Sum(a_n cos n*Pi*x)

 

?

 

I would like to ask your assistance in understanding the following Maple interaction which speaks for itself.

 

> sum(product(k+4-m, m=0..k-1)*z^k ,k=0..j);                                         
                    /    j                 \                                         
                    | --------'            |
                    |'  |  |               |  (j + 1)
                    |   |  |    (j + 5 - m)| z
                    |   |  |               |
                    |   |  |               |
                    \  m = 0               /               1
                    --------------------------------- - -------
                                 4 z - 1                4 z - 1

> series(simplify(subs(j=6, %)), z=0, 16);   
              2       3        4         5         6            7            8
1 + 4 z + 16 z  + 64 z  + 256 z  + 1024 z  + 4096 z  - 1646816 z  - 6587264 z  -

              9              10              11               12               13
    26349056 z  - 105396224 z   - 421584896 z   - 1686339584 z   - 6745358336 z

                    14                 15      16
     - 26981433344 z   - 107925733376 z   + O(z  )

> sum(product(k+4-m, m=0..k-1)*z^k ,k=0..6);
                     6          5         4        3       2
             151200 z  + 15120 z  + 1680 z  + 210 z  + 30 z  + 5 z + 1

> sum((k+4)!/4!*z^k ,k=0..6);
                     6          5         4        3       2
             151200 z  + 15120 z  + 1680 z  + 210 z  + 30 z  + 5 z + 1

 

This was with Maple 18 (X86 64 LINUX).

 

Best regards, Marko Riedel

 

 

Population at point A is 500. Point B 200. See pics.

where is the best point to meet such that the total distance is minimized. Can only go "taxi way", no diagonals allowed.

[the answer is (5,5).

Solution given: sumPop/2=~7 units. Left-right sum7 occurs at C, x=5. Bottom-top sum7 occurs at B, y=5].

there must be a better (Maple) way...

I define unit vectors as

delta[1] := Vector(3, {(1) = 1, (2) = 0, (3) = 0})

delta[2] := Vector(3, {(1) = 0, (2) = 1, (3) = 0})

delta[3] := Vector(3, {(1) = 0, (2) = 0, (3) = 1})

Then I manually take the dot product as

Eq3 := delta[1].delta[1]+delta[1].delta[2]+delta[1].delta[3]+delta[2].delta[1]+delta[2].delta[2]+delta[2].delta[3]+delta[3].delta[1]+delta[3].delta[2]+delta[3].delta[3]

and get

Eq3 := 3

But when I do this

Eq4 := sum(sum(delta[i].delta[j], j = 1 .. 3), i = 1 .. 3)

I get

Eq4 := Vector(3, {(1) = Vector(3, {(1) = 1, (2) = 1, (3) = 1}), (2) = Vector(3, {(1) = 1, (2) = 1, (3) = 1}), (3) = Vector(3, {(1) = 1, (2) = 1, (3) = 1})})

How can I make Maple give me the first result using the sum command?

 

Dear Feinds,

How can I compute a double summation of the following form in Maple.

                                                      ∑5m=1  ∑j+k=m-1 (2m (Dk(a_m*f)) (Dj(f)))

where Drepresents nth order derivative.

Thank you for your help!

EDIT 1

Summand added

EDIT 2

Function "f" in the first derivative is changed to "a_m*f" where a_m (variable coefficients) represents any function of x.

First of all thank you so much for all the nice answers.

Here, the notation a_m doesn't work as I was expecting and then I thought let's just make it a(m) for simplicity, it seemed to work fine but unfortunatelyassumes it as a constant function. How can I rectify this problem?

 

I have this simple sum equation: plot(y=sum(0.5^(n), n=1..x) It does not work for me at the moment, and my brain is getting fried from thinking at it. I think it might be because im using the x inside the sum parantheses, but it might also just be me having overlooked something or made a stupid little mistake, but could you please just help me?

 

Thank you in advance

sum(xj*(sum(yi, i = k .. n)), j = k .. n)

How do I solve this? Can anone help?

Here x and y both are variables.

I am working on a problem involving sums in Maple and I find Maple's facilities lacking.

Specifically; I want to convert the square of a sum into a sum of squares plus the cross terms (which is a subtask of a larger problem). So I start with

sum(E[n],n=1..N)^2;

and immediately get stuck as I do not find any command that does anything with it. The expansion of this is known and easy to derive:

sum(E[n],n=1..N)^2 = sum(E[n]^2,n=1..N) + 2*sum(sum(E[m]*E[n],m=1..n-1),n=1..N);

Maple knows nothing about this relation. I have checked out packages like SumTools but have not found anything useful for this purpose. Quite some time ago I have had difficulty distributing a sum over the elements of its expression; this was answered here and involved a custom function.

Does a package exist that has these kinds of conversions, or do I need to roll my own? It seems a general enough issue that I would expect functions for this to exist.

TIA,

Mac Dude

I have an expression like this (from an earlier computation):

2*(sum(A*cos(omega*t)^2+cos(omega*t)*B*sin(omega*t)-cos(omega*t)*ymeas(t), t));

I want to distribute the sum over the terms in the expression, i.e.

sum(A*cos(omega*t)^2,t)+sum(cos(omega*t)*B*sin(omega*t,t)+sum(cos(omega*t)*ymeas(t), t)));

I suspect defining a rule and using applyrule should be the way to go, but for the heck of it I can't figure how to do it. The best I can manage is getting the Maple kernel hung with the following construct:

distSum:=sum(A::algebraic+B::algebraic+C::algebraic,D=algebraic)=sum(A,D)+sum(B,D)+sum(C,D);

applyrule(distSum,(5)); # (5) referrs to the expression on line 2 (and it is a proper label in my Maple wrkbook).

I have asked similar questions before and gotten answers; but I am not able to find what I need in MapePrimes (or my faorites, for that matter).

Thanks for any help,

Mac Dude

 

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