Mr. Marko Riedel

## 390 Reputation

11 years, 320 days
B.Sc. Computer Science UBC 1994, M.Sc. Computer Science UofT 1996.

## bivariate generating function...

Greetings to all.

Just a quick question, probably something obvious, please bear with me Your patience is appreciated.

As part of solving a posted problem at math.SE it became necessary for me to compute the bivariate generating function

sum(sum(binomial(2*q,n-1)*z^q/q!, q=0..infinity)*w^n,n=1..infinity)

The correct answer (in fact a simple computation) is

w exp(z(w+1)^2).

When asked to compute this sum with the command shown, Maple produces

hypergeom([], [], z) w

My question for you is, how does this represent the above answer that I computed manually? When I simplify the hypergeometric, Maple says

w exp(z)

which would appear to be the wrong value. Could someone enlighten me regarding this discrepancy?

BTW there seems to be no tag "hypergeometric" and I don't have enough points to create it.

Best regards, Marko Riedel

## simple asymptotic expansion...

Maple

Dear friends,

I wonder how I would go about calculating the asymptotic expansion of

sum(5^j/j, j=1..m+1)?

The motivation for this calculation can be found here. The correct answer is

5/4 5^(m+1)/(m+1).

The classic asympt and the one from multiseries both fail on this one.

Thanks,

Marko Riedel

## computing a residue...

Maple

Dear friends,

I ran into another problem while using Maple to do residue calculus. The following call

residue(1/x^(1/3)/(x^2+2*x*cos(phi)+1), x=-exp(I*phi));

returns zero -- it does not recognize the residue. On the other hand, if I do a subsitution like this

subs(x=-exp(I*phi), 1/x^(1/3)/(x^2+2*x*cos(phi)+1));

followed by

convert(%, trig); simplify(%);

then I get a divide by zero error, which shows that the...

## constant of integration...

Maple

Dear friends,

I have a basic question concerning Maple 15 (X86 64 LINUX). In fact it is so simple it is almost embarassing! Here it is.

When we do integration in a basic calculus class we learn that when integrating polynomials and series the constant that appears during the integration is usually taken to be zero, as polynomial and Laurent series terms will only produce powers and logs, but no constant. Of course the choice of constant does not influence definite integrals, as it cancels.

## tt tags and your web form editor...

Hello there,

I tried using your HTML window that can be activated from your editor to write a post. I intended to use HTML TT tags to display some MAPLE input, and everything previewed fine. However when I looked at the actual post after I submitted, the content between the TT tags had disappeared. Tried it twice. I have a feeling you are validating your HTML but some regex does not know about the TT tags and eliminates them.

Best regards,

Marko Riedel

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