Items tagged with summation

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I did dummy indices implication using add command as below. is it OK or there are mistakes?

Is there another way to imply dummy index summation in maple instead of using add command?

any suggestion???

restart

II := 9:

JJ := 9:

with(LinearAlgebra):

 

 

F := add(add(add(add(R[i, m]*R[k, m]*(U[i, j]*U[k, j]+U[i, j]*V[k, j]+V[i, j]*V[k, j]+W[i, j]*W[k, j])/((2*m+1)*(2*j+1)), i = 0 .. II), k = 0 .. II), m = 0 .. II), j = 0 .. JJ):

EqU := seq(seq(diff(F, U[i, j]), j = 0 .. JJ), i = 0 .. II):

EqV := seq(seq(diff(F, V[i, j]), j = 0 .. JJ), i = 0 .. II):

EqW := seq(seq(diff(F, W[i, j]), j = 0 .. JJ), i = 0 .. II):

var := [seq(seq(U[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(V[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(W[i, j], j = 0 .. JJ), i = 0 .. II)]:

NULL

sys := [EqU, EqV, EqW]:

Aa, bb := GenerateMatrix(sys, var):

Aa

RTABLE(18446744074191847422, anything, Matrix, rectangular, Fortran_order, [], 2, 1 .. 300, 1 .. 300)

(1.1)

``


 

Download Mesal.mw

 

 

 

updated

after refer from

https://en.wikipedia.org/wiki/List_of_representations_of_e

exponential1 := sum((1/n!), n=0..infinity);
exponential1 is not a decimal number, it is exp(1)
 
hoyeung1:= sum((Int(exp(LambertW(1/(-1+x))*(-1+x)), x)), x=0..infinity);
 
hoyeung2:= sum((Int(exp(LambertW(1/(-1+x!))*(-1+x!)), x)), x=0..infinity);
 
how to evalute hoyeung1 or hoyeung2 as a decimal number?
 
how to evalute hoyeung^x as a decimal number function is func1 := proc(x) return hoyeung^x end proc:
 
but i do not know whether sum((Int(exp(LambertW(1/(-1+x))*(-1+x)), x))*m^x, x=0..infinity) = hoyeung^x
 
can limit(1+(Int(exp(LambertW(1/(-1+x))*(-1+x)), x)))^x, x=infinity) = hoyeung^1 ?
Lee := (-1+Int(exp(LambertW(1/(-1+t))*(-1+t)), t=1..x))/(Int(exp(LambertW(1/(-1+t))*(-1+t)), t=1..x));
sum(unknown, n=1..infinity) = Lee
 
how to find unknown?

I am trying to evaluate the following summation which gives the result 0. But I think answer is not correct.
 

restart; x := 0; evalf(Sum(Sum(x^(q-p), p = 0 .. q), q = 0 .. 10))

0.

(1)

``


 

Download zero.mw

doubt.mw

Equation21v2.mw

 

Hi,

When I do the derivation of a summation in order to one single term should not the result come out of the summation in the example attached in the file doubt? for example the derivative should not have yielded Ci and not the summation of Ci because for example if want the derivative in order to y1 it should be only C1 and not the summation of Ci.

 

The same happen when I go to a more complex case like in the file Equation21v2, should the result in the last double summation before T drop the summation over i to NC?

 

Many thanks in advance for your help!


 

Hello everybody,

I am trying to solve the following integral which also has summation but it gives me strange results. Do anyone know if I am doing something wrong?

The equation is in black and the strange result is in blue.

Thank you !

Dear All

Please see my query below:


 

Suppose I have a expression whose terms are in summation:

sum(P[n]*xi^n, n = 0 .. infinity)+(sum(P[n]*xi^n, n = 0 .. infinity))^2+sum(P[2*n+1]*P[2*n]*xi^n, n = 0 .. infinity)

sum(P[n]*xi^n, n = 0 .. infinity)+(sum(P[n]*xi^n, n = 0 .. infinity))^2+sum(P[2*n+1]*P[2*n]*xi^n, n = 0 .. infinity)

(1)

diff(sum(P[n]*xi^n, n = 0 .. infinity)+(sum(P[n]*xi^n, n = 0 .. infinity))^2+sum(P[2*n+1]*P[2*n]*xi^n, n = 0 .. infinity), xi)

sum(P[n]*xi^n*n/xi, n = 0 .. infinity)+2*(sum(P[n]*xi^n, n = 0 .. infinity))*(sum(P[n]*xi^n*n/xi, n = 0 .. infinity))+sum(P[2*n+1]*P[2*n]*xi^n*n/xi, n = 0 .. infinity)

(2)

In above summation, how I can write specific term ? For example, how I can display term for n = 2etc.

NULL


 

Download Summation.mw

Consider the expression infinityn=1 (-1)n ebeta*n/n2

 

1. Find the symbolic value of this sum.

2. Find an approximation for the value when beta= -2.

3. Build a function to calculate an approximation for the value of the given expression for

any value for beta

 

Hi, so I have few problems here. I need to;

Create a MxN Matrix/Lattice, where N and M can be any positive integer, that contains a random selection of -1/1s at each entry.

Need to sum every entry, then multiply by -1 to find “H”.

Need to multiply each neighbour to find its bond energy, so if it’s the same you get 1 else -1, but only its direct neighbours once, so if it was a 2x2 matrix there would be only 4 values and then sum them.

I don’t seem to be able to set up the code so that it does it for any size matrix, as I only know how to write it out basic for a 2x2. Also, not so important, but I wanted to know if could create a loop that would find every iteration of possible setups i.e. for a 2x1 you can have 1.1, -1.1, 1.-1, -1.-1. And then give the solutions outlined earlier for each of the the possibilities [There being 2MxN ]

Cheers in advance.

Hi,

I have encountered some strange issue with symbolic summation. Would be grateful for any help.

Here is the code (inserted as image):

Symbolic summation of powers of sines & cosines

 

Code in text:

restart;
F:=(n,a,b)->sum(r^(a+b)*cos(2*Pi/n*j+t)^a*sin(2*Pi/n*j+t)^b,j=0..n-1);

F(n,2,2);
F(4,2,2); 

The issue is that symbolic summation produces the formula (for general n) which contradicts the particular case (n=4).

Could somebody explain why this is happening? Is it a bug or am I missing something here?

I have tried all versions of Maple downto 14 - same situation.
Also Mathematica givers the same answer.

Thank you in advance,
Pavel Holoborodko.

--
Multiprecision Computing Toolbox
http://www.advanpix.com/

Hello people in mapleprimes,

I want to distribute limit or Limit to each terms of summation.

Limit(f(a+h)-f(a),h=0);

But, the output is not distributed one, but the same as the input, though

I want it to become Limit(f(a+h),h=0)+Limit(f(a),h=0), or

Limit(f(a+h),h=0)+f(a).

Isn't there any way for it, other than a trivial one that is

subs(Limit(f(a+h)-f(a),h=0)=Limit(f(a+h),h=0)+Limit(f(a),h=0),Limit(f(a+h)-f(a),h=0));

?

I hope someone will teach me.

Thanks in advance.

taro

 

Hello

Any idea about the summation of Fibonacci sequence

 

Fibonacci.mw

 

Best regards

 

How do I multiply the 4x into the summation to get  (Sum(4*n*a[n]*x^(n), n = 0 .. infinity))  and same idea for the 3rd third?

Also, how do I go from   Sum(a[n-2]*x^(n-2), n = 2 .. infinity)  to  Sum(a[n]*x^(n), n = 0 .. infinity)  by manipulating the indices?

 

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!!

 

I'm trying to solve a system of equations thats expressed as a summation (the original has the summation symbol as opposed to 'sum'):

d_actual := solve(W_actual = sum(W_guess(def-asp_rad_inverse[i], E, asp_rad[i]), i = 1 .. n), def);

When n<5, I get an answer after a few seconds, but when n is higher, the program sits and 'evaluates' forever...I've waited up to 30 min. 

Background:

I have a plate with a number of hemispheres on the surface (# of impacted hemispheres given a force = n). Each has a unique radius and they're listed from largest to smallest in 'asp_rad[]'. I have an equation for the deflection of a single hemisphere as a function of Force and material properties that I have rearranged with respect to Force (W_guess(deflection, E, r)). There's an opposing plate that stays parallel to the original plate while pushing down on the asperities with Force W_actual. The total deflection of the opposing plate is the sum of: 1) the difference between the tallest radius and the impacted radius in question (asp_rad_inverse[]), and 2) the deflection of the impacted radius in question. 

I'm attempting to solve for the total deflection of the opposing plate via solving for the 'def' in the summation above, but when I run it, the program is not able to compute a solution.

Thanks in advance.

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