That was interesting!

Here is another way of doing that,

ind:=proc() local a, a1; option remember; 
try cat(a,nops(op(op(4,eval(procname))))+1) catch: a1 end end:
evalindets[flat](f,'float',ind);

This way the assigned values can be restored using

op(op(4,eval(ind)));

[0.2467414433 = a5, -1.751336299 = a1, -0.3611166740 = a3,
-0.5457363063736358 = a2, -0.2061949348454455 = a4]

Alec

That was interesting!

Here is another way of doing that,

ind:=proc() local a, a1; option remember; 
try cat(a,nops(op(op(4,eval(procname))))+1) catch: a1 end end:
evalindets[flat](f,'float',ind);

This way the assigned values can be restored using

op(op(4,eval(ind)));

[0.2467414433 = a5, -1.751336299 = a1, -0.3611166740 = a3,
-0.5457363063736358 = a2, -0.2061949348454455 = a4]

Alec

That's absolutely true.

Perhaps, forum moderators should have a way to reach Will, and regular members should have a way to reach forum moderators (for example, have their email addresses listed in some other place - on the main Maplesoft site, for instance.)

Still, there is a problem with graveyard shift. What to do when all the moderators and Will are sleeping?

Alec

I'll post more details later in my blog. There are a lot of other interesting things related to that (other identities, rational points on elliptic curves etc.)

Maple seems to have more tools for differential equations than for algebraic equations :)

Some related stuff can be found in A.M. Perelomov's article.

Alec

I'll post more details later in my blog. There are a lot of other interesting things related to that (other identities, rational points on elliptic curves etc.)

Maple seems to have more tools for differential equations than for algebraic equations :)

Some related stuff can be found in A.M. Perelomov's article.

Alec

Normally, at least 2 or 3 people would monitor the site (including site administration), so that it would be monitored continuously. Probably, as Axel Vogt mentioned in another post, Maplesoft, being a rather small software company, just doesn't have enough staff for that.

Alec

Axel,

Thank you!

This award came as a big surprise to me. Anyway, it is a very nice gesture from the company.

Unfortunately, I really don't have much free time. I posted in May just because I got sinusitis and was feeling rather sick - couldn't go out of the house, or do anything serious.

Alec

Georgios,

Thank you very much!

I think, you provided much more student help in May than me.

Regards,
Alec Mihailovs, PhD
Mihailovs, Inc.

Alejandro,

That's a very nice idea!

I got them purely algebraically - using algebraic equations instead of differential.

The topic started from equation 1/sqrt(u+c) + 1/sqrt(u-c) =1.

I noticed that u = 1 + 3*hypergeom([-1/2,1/4,3/4], [1/3,2/3], -4*c^2/27) gives the solution of it (that is unique, because the l.h.s is increasing). That can be proven using identity (4) and the identity obtained from (4) by replacing c with -c.

Now, thinking about the original equation as r + (1-r) =1, we get c = (1/r^2 - 1/(1-r)^2)/2 and u = (1/r^2 + 1/(1-r)^2)/2.

Substituting that in the hypergeometric formula for the solution, we get identity (1).

Alec

Alejandro,

That's a very nice idea!

I got them purely algebraically - using algebraic equations instead of differential.

The topic started from equation 1/sqrt(u+c) + 1/sqrt(u-c) =1.

I noticed that u = 1 + 3*hypergeom([-1/2,1/4,3/4], [1/3,2/3], -4*c^2/27) gives the solution of it (that is unique, because the l.h.s is increasing). That can be proven using identity (4) and the identity obtained from (4) by replacing c with -c.

Now, thinking about the original equation as r + (1-r) =1, we get c = (1/r^2 - 1/(1-r)^2)/2 and u = (1/r^2 + 1/(1-r)^2)/2.

Substituting that in the hypergeometric formula for the solution, we get identity (1).

Alec

3F2 identities, is, certainly, a very interesting topic. I can suggest a few more,

(1)              hypergeom([-1/2,1/4,3/4], [1/3,2/3], -(1-2*r)^2/27/r^4/(1-r)^4) = (1-2*r+4*r^3-2*r^4)/6/r^2/(1-r)^2  for 0<r<1.

In particular, for r=1/3,

(2)             hypergeom([-1/2,1/4,3/4], [1/3,2/3], -27/16) = 37/24.

(3)            hypergeom([-1/4,1/2,1/4], [1/3,2/3], x)^2 = 1/3 + (2/3)*hypergeom([-1/2,1/4,3/4], [1/3,2/3], x);

(4)           (1-(1/8)*c*hypergeom([5/4,3/4,1/2], [5/3,4/3], -4*c^2/27))^2 * (1+c+3*hypergeom([-1/2,1/4,3/4], [1/3,2/3], -4*c^2/27)) = 4.

...

Alec

3F2 identities, is, certainly, a very interesting topic. I can suggest a few more,

(1)              hypergeom([-1/2,1/4,3/4], [1/3,2/3], -(1-2*r)^2/27/r^4/(1-r)^4) = (1-2*r+4*r^3-2*r^4)/6/r^2/(1-r)^2  for 0<r<1.

In particular, for r=1/3,

(2)             hypergeom([-1/2,1/4,3/4], [1/3,2/3], -27/16) = 37/24.

(3)            hypergeom([-1/4,1/2,1/4], [1/3,2/3], x)^2 = 1/3 + (2/3)*hypergeom([-1/2,1/4,3/4], [1/3,2/3], x);

(4)           (1-(1/8)*c*hypergeom([5/4,3/4,1/2], [5/3,4/3], -4*c^2/27))^2 * (1+c+3*hypergeom([-1/2,1/4,3/4], [1/3,2/3], -4*c^2/27)) = 4.

...

Alec

When I first noticed that (weekend outages), I thought to myself - another bad rep for Maplesoft. But then, thinking more people oriented, I get another thought - "why not?". Will seems to be the only person maintaining this site, and he has the right to have some (especially weekend) breaks. It is better to see the MySQL problems than some spam. And couple of years ago, when I was more active here than now, there were a lot of spam posts that the site administrator had to deal with.

Alec

Thank you, guys!

You, certainly, have a good sense of humor!

From other point of view, considering that being more like a lifetime achievements award rather than this May award, that may be deserved.

Thanks again,

Alec

Axel,

You are right that I shouldn't suggest anybody without consulting with him first. It's just I don't have much time at the moment - and I am going to leave this site again for some time. This may be the last post. I just wanted to say what I wanted to say before leaving.

Alec