Question: taking limit with assume on indexed variable on limit expression

I am also having trouble with limits when I have indexed
variables.   That is, how do I tell Maple to assume every element of
an indexed variable is positive?

uxb3% maple < te7a

    |\^/|     Maple V Release 3 (Governors State University)



Here, I show that normal limits work.
> int (exp(-x^2),x=3..infinity);

                                1/2         1/2

                          1/2 Pi    - 1/2 Pi    erf(3)



> assume(a>0);

> int(exp(-a*x^2),x=3..infinity);

                             1/2         1/2         1/2

                           Pi          Pi    erf(3 a~   )

                       1/2 ----- - 1/2 ------------------

                             1/2                1/2

                           a~                 a~



But what if the coefficient inside the exponent is indexed, and I need to
let Maple know it positive?

> assume(b>0);

> int(exp(-x^2*b[i]),x=3..infinity);

bytes used=1000092, alloc=786288, time=0.08

                           1/2          1/2            1/2            1/2

                         Pi    erf(b~[i]    x)       Pi    erf(3 b~[i]   )

      limit          1/2 --------------------- - 1/2 ---------------------

      x -> infinity-                 1/2                         1/2

                                b~[i]                       b~[i]

Notice that Maple leaves the limit expression.

I also tried using for loops; This is not ideal as I want a general expression
in terms of whatever indices I have.


> y=array(1..3);
                            y = [ ?[1], ?[2], ?[3] ]

> for i from 1 to 3 do
> assume(y[i]>0);
> od;
Error, (in assume) cannot assume on a constant object