## 25 Reputation

2 years, 172 days

## how to draw this region...

Maple

Hello, consider 0<x<1, 0<y<1 and t >0 (t: fixed)

Let the region:
R={(x,y) | x*(1-y)/y*(1-x) < t}

How can I draw the region R in Maple. thanks.

## Slow series summation...

Hello, I trying to sum up a series which involves several binomial terms, Maple simply gets stuck and give no results. I think I am not being smart to improve Maple performance. Please, see my code below:

>n1 := 423; x := 16; n2 := 81; y := 35; s1 := 0.1; b1 := 7; beta1 := 2.1; s2 := 0.1; b2 := 7; beta2 := 2.1;

>A := (h, v) -> Sum(Sum(binomial(n1 - x, j)*binomial(n2 - y, l)*(-1)^(j + l)*GAMMA(s1 + h + 1)*GAMMA(s2 + v + 1)*(-1)^(h + v)*(beta1 - 1)^h*(beta2 - 1)^v/(h!*GAMMA(s1 + 1)*v!*GAMMA(s2 + 1)*(x + b1*s1 + j + b1*h + y + b2*s2 + l + b2*v)*(r + x + b1*s1 + j + b1*v)), j = 0 .. n1 - x), l = 0 .. n2 - y);

>B := (h, v) -> Sum(Sum(binomial(n1 - x, j)*binomial(n2 - y, l)*(-1)^(j + l)*GAMMA(s1 + v + 1)*GAMMA(s2 + h + 1)*(-1)^(h + v)*(beta1 - 1)^v*(beta2 - 1)^h/(v!*GAMMA(s1 + 1)*h!*GAMMA(s2 + 1)*(y + b2*s2 + l + b2*h + x + b1*s1 + j + b1*v)*(y + b2*s2 + l + b2*h - r)), j = 0 .. n1 - x), l = 0 .. n2 - y)

>f := (r, upto) -> sum(sum(A(h, v) + B(h, v), v = 0 .. upto), h = 0 .. upto);

>f(0,30);

Summing up to 30 is very slow, I have left it running over many hours and no result was provided. Could we improve the way it is summing up? thanks in advance.

## Help on: Error, bad index into Vector ...

Maple

Hello, I am trying to evaluate this summation, but it keeps giving me a "Error, (in H) bad index into Vector", I can`t find the problem in function, would somebody helps? thanks.

My function:

with(linalg); H := proc (z, aa, AA, bb, BB, m, n, p, q) mu0 := sum('BB'[i], i = 1 .. q)-(sum('AA'[i], i = 1 .. p)); beta0 := (product('AA'[i]^(-'AA'[i]), i = 1 .. p))*(product('BB'[i]^(-'BB'[i]), i = 1 .. q)); if z <> 0 and 0 < mu0 or 0 < abs(z) and abs(z) < 1/beta0 and mu0 = 0 then do s := Vector([seq(-('bb'[i]-v)/'BB'[i], i = 1 .. m)]); Hz := sum(sum((product(('`if`')(i <> h, GAMMA('bb'[i]+'BB'[i]*'s[h]'), 1), i = 1 .. m))*(product(('`if`')(i <> h, GAMMA(1-'aa'[i]-'AA'[i]*'s[h]'), 1), i = 1 .. n))*(-1)^v*z^(('bb[h]'+v)/'BB[h]')/(('`if`')(m < q, product(('`if`')(i <> h, GAMMA(1-'bb'[i]-'BB'[i]*'s[h]'), 1), i = m+1 .. q), 1)*`if`(n < p, product(('`if`')(i <> h, GAMMA('aa'[i]+'AA'[i]*'s[h]'), i = n+1 .. p), 1), 1)*factorial(v)*'BB[h]'), h = 1 .. m), v = 0 .. 10) end do end if; return Hz end proc

>evalf(H(.547, Vector([-23-j]), Vector([.5]), Vector([0, -24-j]), Vector([1, .5]), 1, 1, 1, 2))

## Improving summation performance...

Maple

Hello, I have the following (nested) summation:

add(binomial(196, j)*0.5^(32.1+j)*add(binomial(109, l)*(-1)^(j+l)*add(0.5^(3.1*h)*GAMMA(-4.1+h)*GAMMA(9.3170731707317073170731707317073170731707317073170+.24390243902439024390243902439024390243902439024390*l+.24390243902439024390243902439024390243902439024390*j+.75609756097560975609756097560975609756097560975610*h)/(factorial(h)*(10.354838709677419354838709677419354838709677419355+.32258064516129032258064516129032258064516129032258*j+h)*GAMMA(.24390243902439024390243902439024390243902439024390*j+.24390243902439024390243902439024390243902439024390*l+15.417073170731707317073170731707317073170731707317+.75609756097560975609756097560975609756097560975610*h)), h = 0 .. infinity), l = 0 .. 109), j = 0 .. 196)

But it takes ages to sum h up to 80, for example. I was wondering whether we could improve to gain time. any ideas?

Maple 2018

Hello,

I noted that add and 'add' can give different result, can somebody help me understand it?  Consider the code below:

>phi1 := GAMMA(-(1/2)*vst-8.333500000-(1/2)*r)*GAMMA((1/2)*vst+21/2+(1/2)*r); phi2 := GAMMA(16.66700000+r-2*vst)*GAMMA(2.166500000+vst); xi1 := -vst; xi2 := 16.66700000+r-2*vst; z := 37.52950222; K := 9.846618489*10^(-38)*33.330^(.5000000000*r+10.)

### Then I have the following sums (they were supposed to give the same results):

>f := unapply(K*add(phi1*(-1)^vst*z^(-xi1)/factorial(vst)+phi2*(-1)^vst*z^(-xi2)/(.5*factorial(vst)), vst = 0 .. 10000), r):

>g := unapply(K*'add'(phi1*(-1)^vst*z^(-xi1)/factorial(vst)+phi2*(-1)^vst*z^(-xi2)/(.5*factorial(vst)), vst = 0 .. upto), [r, upto]);

# I am interested in the following quantities:

>evalf(f(1)/f(0));

-6.265883733

>evalf(g(1,10000)/g(0,10000))

25.80438437

That seems very strange to me, why maple gives different results?

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