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MaplePrimes Activity

These are questions asked by macchianera

I need to solve this integral:

assume(1 > q, q > 0, 1 > p, p >0, q > p);
lambda21 := int(int(int(((xs-xr)^2+(ys-p)^2)*xr/(xs-xr),xr=0..(2-p)*xs/(2-ys)),xs=0..q),ys=0..p);

The result in Maple 8 is:

lambda21 := -1/96*q^2*(256*ln(2)-256*ln(2-p)-48*p^3*ln(2)+16*p^3*ln(p)-384*p*ln(2)+384*p*ln(2-p)+32*p^3*ln(2-p)+192*p^2*ln(2)-192*p^2*ln(2-p)+q^2*p^3-4*q^2*p-128*p-48*lambda21^3+160*p^2);

The result in Maple 9.5 is:

<p>I'm a beginner and I need to implement this recursive function with Maple:</p>
<p>$$\left\{\begin{array}{c}<br />
Z(1)=(1-p_a)(1-p_b)\\<br />
Z(i)=((1-p_a)(1-p_b))^{\left(\frac{p_a}{1-p_a}+\frac{p_b}{1-p_b}\right)^i}\prod_{k=1}^{i-1}(1-Z(k))<br />
<p>where 0<p_a<1 and 0<p_b<1</p>
<p>So I write in Maple:</p>
<p>Z:=(i, pa, pb)->if i=1 then (1-pa)*(1-pb) else (((1-pa)*(1-pb))^((pa/(1-pa)+pb/(1-pb))^i))*product(1-Z(k, pa, pb),k=1..i-1) end if;</p>
<p>When i=1 the function works</p>
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