Symbolic Sum to find a general expression for arbitrary n terms and arbitrary variable definitions

Hello, I have a need to add some terms defined using an index for the index running from 1 to and arbitrary number n.

I have equations similar to (actual equations are too long but the problem is the same):

⋮

where is an arbitrary number associated with

Goal:

I wish to find the average of these terms running from

I know I can use symsum for accomplishing this task.

syms x m
e = x + p_{m} % I want to know how to define this p_{m}
symsum(e, m, 1, n)

But I have the following question:

Question:

1) How do I define arbitrary symbolic variables 's for each equation. So that when I get the final sum of all the symbolic variables from 1 to n it will contain .

Please provide example code.

[atharva aalok]

Another way of looking at this question would be to generate the following:

where are arbitrary numbers

[atharva aalok]

Ok I got some lead. I got how to create a symbolic variable with an arbitrary name.

syms x n
syms(sprintf('p%s', n)) % Create symbolic variable with name p_{n}
whos

  Name        Size            Bytes  Class    Attributes

  cmdout      1x33               66  char               
  n           1x1                 8  sym                
  pn          1x1                 8  sym                
  x           1x1                 8  sym                

Now the only problem left is to run symsum() and to create a new variable and use it in the sum everytime.

That is to make the declaration in the same statement where I use the variable

Answer 1

[Walter Roberson]

You cannot do that in MATLAB for symbolic limits.

For specific limit, n being a given positive integer, then you would not use symsum for this purpose. Instead,

n = a positive integer 
syms a [1 n]
syms x [1 n]
y = sum(a.*x)

That is, you create vectors or arrays in which each entry is a scalar symbol. You then do vectorized operations, producing a vector or array of definite terms. You then sum() the definite terms.

symsum is not primarily for creating a sum of definite terms: symsum is primarily for trying to find closed formulas for indefinite or infinite summations.

Under no circumstances can you use a symbolic variable as an array index.

[atharva aalok]

Can we not do something like:

syms x k
e = x + syms(sprintf('p%s', k))

Error using syms
Using input and output arguments simultaneously is not supported.

If this is possible then the problem would be solved

[Walter Roberson]

e = x + sym(sprintf('p%s', char(k)))

which would give you the definite term

e = x + pk

if you were to symsum(e, k, 1, n) then the result would be n*x + n*pk

[Walter Roberson]

You need to understand that the parameters to functions are fully evaluated before the function ever sees them

[Walter Roberson]

So what would be passed to the sprintf is not going to be the "current" value of k for a series of values 1 to n: what is going to be passed to sprintf is the unresolved symbol k. So the sprintf would be invoked once to create literal 'pk' which gets you symbol pk and x + pk would get passed to symsum where that pk has no more connection to k than x does.

symsum will then internally subs(EXPRESSION, k, n) and subs(EXPRESSION, k, n+1) and possibly other terms and will work with those to try to come up with a closed formula. The difference would be 0 because x+pk contains no reference to k so symsum will predict the formula (x+pk) * (n-1+1). symsum will not add up the terms one by one.