CODEWITHSUNDEEP
matlabfunctionsymbolic-math
A Doe
A Doe

Reputation: 301

Matlab - define a function that is a summation

I am trying to define I function which I will derivate later and the function is

enter image description here My code is as below:

syms i q j
syms f(i,q)
f=symsum(((1-q)^(i-j))*j*q,j,0,i)

The f I get shows me 4 terms but in fact I do not know this number. Is it correct or how do I enter this correctly?

Upvotes: 1

Views: 346

Answers (1)

Daniel1000
Daniel1000

Reputation: 797

First of all, please don't use i and j, because they correspond to the imaginary unit; that causes misunderstandings. 

syms N q k
syms f(i,q)
f=symsum(((1-q)^(N-k))*k*q,k,0,N)

piecewise(q == 0, 0, q ~= 0, (q + N*q - q*(1 - q)^N + (1 - q)^N - 1)/q)

The result is a piecewise, and it says that the result is 0 if q is 0, and otherwise the formula given on the right.

You can also evaluate Sum[(1 - q)^(M - k) k q, {k, 0, M}] with WolframAlpha, where you get the same result. As you see, your formula can be written without the sum. You get the derivative with D[Sum[(1 - q)^(M - k) k q, {k, 0, M}],q] on WolframAlpha.

Upvotes: 3

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