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


The only variable is 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!


Summand added


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


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.


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:


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


Below is a Maple ws describing the problem. I have some fixed values pr0 and pr1, and a four variations of a function "pdf". The problem is that when I use the function in a sum (either the "sum" function or the sigma notation), the result is different than if I write out the sum explicitly. It's very puzzling as to why they woudl be different in the first place, but even more strange is that the different versions have *different* deltas. Even version 3, with a delta of 10^-100 is too much for my application (moreover the delta gets larger when I sum over more terms).


In the worksheet below, I compare "sum(f(x),x=3..3)" to "f(3)". I expect this should always be identically 0, but that is not true for any of the four versions of my function. (The same is true for "Sum(f(x),x=3..3)".) However, "sum(f(3),x=3..3)" *is* (blessedly) identically "f(3)". What gives?


pr[0] := .499999999999999999999852096538403821434745813543502066245832554193147476551830440227306019620687012523264913799181385911651886999607086181640625:

pr[1] := .43394228095117646589504674154844928036961264935215813494922283329725383492977635163048065719014507668417797436877236805230495519936084747314453125:

pr0 := .499999999999999999999852096538403821434745813543502066245832554193147476551830440227306019620687012523264913799181385911651886999607086181640625:

pr1 := .43394228095117646589504674154844928036961264935215813494922283329725383492977635163048065719014507668417797436877236805230495519936084747314453125:

pdf1 := proc (x) local j, prob, y; prob := 1; y := x; for j from 0 to 1 do if `mod`(y, 2) = 1 then prob := prob*pr[j] else prob := prob*(1-pr[j]) end if; y := floor((1/2)*y) end do; return prob end proc:

Maple doesn't always like subscripted variables. Is that the problem?

pdf2 := proc (x) local prob, y; prob := 1; y := x; if `mod`(y, 2) = 1 then prob := prob*pr0 else prob := prob*(1-pr0) end if; y := floor((1/2)*y); if `mod`(y, 2) = 1 then prob := prob*pr1 else prob := prob*(1-pr1) end if; return prob end proc:

Maybe it's the binary expansion that's the issue

pdf3 := proc (arr) options operator, arrow; product(arr[2-j]*pr[j]+(1-arr[2-j])*(1-pr[j]), j = 0 .. 1) end proc:

No procedures, no arrays

pdf4 := proc (x) options operator, arrow; (`mod`(x, 2))*pr0+(1-(`mod`(x, 2)))*(1-pr0)+(`mod`(floor((1/2)*x), 2))*pr1+(1-(`mod`(floor((1/2)*x), 2)))*(1-pr1) end proc:

evalf[100](sum(pdf1(i), i = 3 .. 3)-pdf1(3));








evalf[100](sum(pdf2(i), i = 3 .. 3)-pdf2(3));





evalf[100](sum(sum(pdf3([i1, i2]), i2 = 1 .. 1), i1 = 1 .. 1)-pdf3([1, 1]));





evalf[100](sum(pdf4(i), i = 3 .. 3)-pdf4(3));











I would like to pay attention to an article " Sums and Integrals: The Swiss analysis knife " by Bill Casselman, where the Euler-Maclaurin formula is discussed.  It should be noted all that matter is implemented in Maple through the commands bernoulli and eulermac. For example,


eulermac(1/x, x);


eulermac(sin(x), x, 6);

BTW, as far as I know it, this boring stuff is substantially used in modern physics. The one is considered in

Ronald Graham, Donald E. Knuth, and Oren Patashnik, Concrete mathematics, Addison-Wesley, 1989.

The last chapter is concerned with the Euler-MacLaurin formula.


I have calculated coefficients in maple using a "for...end do" command. For example,

for n from 0 to 1 do A[n] = int(((2*n+1)*(1/2))*simplify(LegendreP(n, cos(theta)))*sin(theta), theta = 0 .. (1/2)*Pi) end do;

A[0] = 1/2

A[1] = 3/4


Here, I can calculate as many coefficients as I want. But, how do I use these coefficients in the following line? For example, I need to calculate a summation. But for each term in the summation, I want to input the coefficients above to the corresponding term in the sum. So. the following summation


will automaticlly attach the numerical values of the coefficients calculated above to the corresponding term in the sum.


I hope this makes sense.

Hi, I'm having a problem regarding this equation:
                                                           sum(v(i), i = 1 .. 28)

where, v is a Data Table created under the Components Tab with 28 Rows, and 1 Column.

I keep on getting an error of: 

                                                     Error, unsupported type of index, i

I didn't use or declare 'i' in any part of the program.

Thank you for your help! 

Let M and K be given positive integers.

I struggle with how to write efficiently this formula in Maple,mainly because it sums over *pairs* of integers K1 and K2, with the given property that "K1+2*K2=K":




sum { M!/(M-K1-K2)! * K!/(K1! * K2)! * 1/M^K * 1/2^K2 : such that K1 + 2*K2 = K}

The "!" means factorial.

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