MATLAB Answers

Reducing or simplifying the **symbolic** product of two integrals

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Michele Giugliano
Michele Giugliano 29 Jul 2014
I wish using the Symbolic toolbox to guide me in rather simple but tedious work. Part of the formulae I deal with includes the square of a generic integral (or the product of two integrals):
syms t xi h(t) a = int(h(xi), xi, 0, t) pretty(a*a)
QUESTION: Is there any command that I can use to have MATLAB deriving the following expansion (where eta is a symbolic variable of course)
int(int(h(xi), xi, 0, t) * h(eta), eta, 0, t)
i.e., automatically recognising that the product of the above integrals is the double/iterated integral of the product??
That would simplify greatly my life! Without it I am frustrated and resorted to paper and pen: I must in fact anyway evaluate the expected value of the generic quantities h(xi) as random variables and having MATLAB just simplifying the expression a tiny bit would have helped.


Christopher Creutzig
What simplify currently cannot do is to rename your bound variable eta to xi at the right time. You may need to explicitly tell it to do so; assuming you only have eta as a bound variable (such that it can be renamed at will wherever it appears), the following may help:
>> syms h(xi) eta t
>> a = int(h(xi), xi, 0, t)^2 - int(int(h(xi), xi, 0, t) * h(eta), eta, 0, t);
>> subs(expand(a), eta, xi)
ans =

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