How to make a serie ?

Question

Yamina chbak 2020-12-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/695455-how-to-make-a-serie

编辑： Yamina chbak 2020-12-18

采纳的回答： Walter Roberson

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Hi, i need to write a sum of serie :

with b_k= (k+1)^2-(k)^2 and u^(m-k) is the numerical solution approximation u(x,t_m-k) for k=1,...m-1 and m=1,....,20

for m=1:20
syms k u
b(k)=(k+1)^2-k^2;
F=symsum((b(k)-b(k+1))*u(:,m-k),k,1,m-1)
end
F

but i get error

Necessary I need u(:,m-k)

Please help me

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Answer 1

Walter Roberson 2020-12-16

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https://ww2.mathworks.cn/matlabcentral/answers/695455-how-to-make-a-serie#answer_577665

It is never possible to use a symbolic variable as an index in MATLAB.

You need to create a definite list of values and sum() the list. Or loop adding on to a total.

Note by the way that

and so b(k) - b(k+1) = (2*k+1) - (2*(k+1)+1) = -2

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Walter Roberson 2020-12-17

Sorry, you are changing equations too much. Your equation here is quite different than your equation in your Question, and it is not really reasonable to answer both at the same time as they are too different. What is the question you need answered?

Note: using U(:,m-k) is not equivalent to

as t is obviously a vector of values that as outside observers we need to assume is a real number in ℝ or possibly even in ℂ and cannot assume that t just happens to be linear indices . At the very least it is likely that t starts from 0,

and so is not suitable for indexing. Indeed, since

then k can equal m, and then

would be 0, and that is not a valid matrix index.

Yamina chbak 2020-12-17

编辑：Yamina chbak 2020-12-18

在 MATLAB Online 中打开

You are right !, I'm sorry @Walter Roberson. I just asked my first question in a simple formule of b but your answer is not i want. In fact, it's the same problem with different formule, it's all about calculate the sum of series matrix.

I have a matrix U(:,k). My final question : What is the best way to write the code to calculate sum of series matrix :

?

This what i did before

alpha=0.2;b(0)=1.0;c(0)=2.^(1-alpha)-1;
S=U(:,1);  %initialize of S 
for m=2:20
    for k=1:m
         b(k)=(k+1).^(1-alpha)-k.^(1-alpha); c(k)=(k+2).^(1-alpha)-(k+1).^(1-alpha);
         S=(b(k)-c(k))*U(:,m-k);
    end
end
S