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I want to sum over several variables at once.

 

For example, something like

add(add(add(f(k1,k2,k3),k1=range1),k2=range2),k3=range3);

sums over 3 variables. But this can only be done if I know the number of variables in advance. I want to write a code that will sum over m variables, with m being supplied on demand.

 

Maple can do this for integrals. If I write

int(f(seq(k[i],i=1..m)),[seq(k[i]=range[i],i=1..m)]);

the integral is computed over m variables, for any m.

 

How can something like this be implemented for summation?

 

We know that sum can return an symbolic summation, for example,

 

But sometime the relation of parameters in series cannot be defined easily. And it seems that sum cannot correctly determine the symbolic summation of this kind of series:


Maybe it's due to the value of _C(infinite) is undefined. Does anyone have good idea to compute the symbolic summation of this series?

I'd appreciate any help on this topic. Thank a lot.

sum_cannot_return_symbolic_summation.mw

Hi everyone,

I wanted to plot the fourier series up to a given order of a step function using the code I attached, to change the order I used a sum with upper boundary M. When setting M to a particular value and plotting the function the result is obtained within a second, when on the otherhand using plot(subs(M=11,...),...) it takes close to a minute to produce a picture.

This might be a misuse of subs, in any case, I wanted to share my experience and maybe get an explanation about why this takes that much longer.

Cheers,

Sören

restart

f := proc (t) options operator, arrow; sum(-4*sin((2*n+1)*t)/(Pi*(2*n+1)), n = 0 .. M) end proc

proc (t) options operator, arrow; sum(-4*sin((2*n+1)*t)/(Pi*(2*n+1)), n = 0 .. M) end proc

(1)

plot(subs(M = 11, f(t)), t = 0 .. 2*Pi)

 

M := 11; plot(f(t), t = 0 .. 2*Pi)

 

Download fourier_subs.mw

I have an expression like this:

Since it is linear I want Maple to rewrite it into this:

(with the benefit that Maple then can solve it at least up to a point). i have tried to conceive a rule to do that but got stuck relatively quickly. Does anybody have a way to do this (in some genrality)?

Thanks,

Mac Dude.

 

Hi,

Maybe someone can give me a nice answer without Maple.

I am given a fourier series:
ln|cosx|=Co - sum( (-1)^k/k * cos2kx,k=1..infinity)
and am asked what this tells me about the chevychev series for ln(u).

 

Thanks

Hi,

I have

Let

A:= sum(a[n]*phi(n)+b[n+1]*phi(n+2),n=0..N);

Please, I need to write this sum, using only phi(n), how can I use maple to get the solution.

Thank you very much for any idea.

 

 

 

 

 

 

 

f:=C->sum(x[cat(new,c)],c=1..C);

f(4) # does not give me what i want , which is

x[cat(new,1)]+x[cat(new,2)]+x[cat(new,3)]+x[cat(new,4)];

 

seq(x[cat(new,c)],c=1..4);
convert([%],`+`);

This works. But it's just a simple example to illustrate my problem.

 

Is there a way to fix this 'cat' problem in the procedure 'f'?

 

Thanks,

 

casper

restart:with(plots):

h3:=((1+lambda*m*x/a0+phi*((4/Pi*sum((-1)^(n+1)/(2*n-1)*cos(2*Pi*(2*n-1)*x),n=1..infinity)))));

q:=Q-1:

f:=sin(alpha)/E;

DP3:=Int(f-((q*(k+1)*(k+2))/((1-tau)^(k+1)*((h3^(k+2)))*(k+1+tau)))^(1/k),x=0..1);

E:=0.2:phi:=0.2:alpha:=0.1:k:=1:lambda:=0.1:a0:=0.5:m:=0.1:tau:=0.1:

plot((DP3),Q=0..1,axes=box,linestyle=1,color=[red]);

I am unable to plot DP3 vs Q, not only it take very long time but didn't give any output.

Please have a look.

 

Cheers!

 

 Calculus problem S(n)=1^2+3^2+5^2+...+(2n-1)^2 ?

Hello,

restart:

N := N0-(1/2)*sqrt(2)*sqrt(Pi*Kc/d)*(sum(erfc((1/2)*(L*n+x)/sqrt(d*t))+erfc((1/2)*((n+1)*L-x)/sqrt(d*t)),

n = 0 .. infinity));

N0:=0.2:L:=0.25:Kc:=2*10^(-12):t:=360000:d:=2.010619298*10^(-10):

When I plot N vs x = 0..0.25 then there is no issue

plot(N,x=0..0.25,axes=box);

but when try to use a loop to get the data, Maple cannot evaluate

for x from 0 to 0.25 by 0.01 do

N[x]:=evalf(N0-sqrt(Pi*Kc/(2*d))*sum(((((erfc((n*L+x)/(2*sqrt(d*t))))+erfc(((n+1)*L-x)/(2*sqrt(d*t))))),n=0..infinity)));
end do;

Thanks

  

Cumulative list...

January 11 2014 erik10 341

Dear Maple users

My question is probably simple, but I can't seem to figure out how to do it in a smart way way without using procedures: My task is to create a cumulative list from a list. Ex: From [3,-2,5,1,10,7] I want to create the list [3,1,6,7,17,24]. Every entrance in the new list is the sum of the previous ones including the actual entrance. The Statistics package contain a command named CumulativeSum, but unfortunately a list is not returned ... I hope someone can help doing it is a simple way.

Regards,

Erik

How can I show the expression of the following summation as the output, not 11?

3+7+1

 

Dears 

I want to sum some series by Maple and plotting. The problem is the sum of series are known like

serer.pdf

the problem is the difference between two graphs at the intersection x-axis and y-axis.

Is there any solution for this problem.

Amr

I've been given a question:

Let pn denote the nth prime number. Then p1 = 2, p2 = 3, p3 = 5, p4 = 7, p5 = 11, . . . .

It is known that the infinite sum 1/p1 + 1/p2 + 1/p3 + · · · + 1/pn + · · · = infinity.

Find the smallest positive integer N so that 1/p1 + 1/p2 +1/p3 + · · · + 1/pN−1 + 1/pN > e. [Hint : ithprime(n) generates the nth prime number.]

How do I start off?

Many thanks!

Would really appreciate the help in doing this question!

Pi= infinity Σ n=0 ((120n^2+An+B)/(16^n(512n^4+1024n^3+712n^2+194n+15))) for some positive integers A,B.

Hint: Set A=0 to find B, then find A.

I'm so clueless as to how to do this. THANK YOU!

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