Re: Repeated Integrals

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• Subject: [mg130853] Re: Repeated Integrals
• From: W Craig Carter <ccarter at MIT.EDU>
• Date: Tue, 21 May 2013 00:04:13 -0400 (EDT)
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```Hello,
I thought the poster might be looking for something recursive?

int[0, x_] = Integrate[lFunc[a[0], z] g[z], {z, 0, x}]

int[n_Integer, x_] :=
int[n, x] = Integrate[lFunc[a[n], z] int[n - 1, z], {z, 0, x}]

Craig

On May 20, 13, at 5:04 AM, Bob Hanlon wrote:

>
> Read the documentation for Integrate
>
>
> h[x_, a_] = Integrate[L[y, a] g[y], {y, 0, x}];
>
>
> f[a_, b_, w_] = Integrate[L[x, b] h[x, a], {x, 0, w}];
>
>
> It is not clear what you want to change and how they are to change during
> the N repetitions: a, b, w, or some combination of them? Presumaby you
> would use f[a,b,w] inside a Table perhaps flattening (Flatten) the Table
> results if you prefer the output as a list rather than a matrix. Read the
> documentation for Table and Flatten.
>
>
> sol = Table[f[a, b, w], {a, 2}, {b, {b1, b2, b3}}, {w, 1, 5, 2}] // Flatten
>
>
> Using a capital letter for a user-defined function (e.g., L) or starting
> the name of a user-defined function with a capital letter is not
> recommended.This could result in a conflict (now or in a future version)
> with a built-in Mathematica name or function.
>
>
>
> Bob Hanlon
>
>
>
>
> On Sun, May 19, 2013 at 5:47 AM, <briankolo at gmail.com> wrote:
>
>> I'm fairly new to Mathematica and I'm trying to create an expression for a
>> set of nested integrals. The innermost integral is
>>
>> int[0,x,L(y,a)g(y),dy]
>>
>> Where g(y) is an arbitrary function and a is a parameter. The next
>> integral is
>>
>> int[0,w,L(x,b)h(x,a),dx]
>>
>> Where b is a parameter and h(x,a) is the result of the previous integral.
>>
>> The process then repeats N times. Is there a simple way to express this in
>> Mathematica?
>>
>>
>>
>

```

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