That seems to be working better without functions,

delta,m:=0,1;
A := (-m^2-2*x*m+1)/(sqrt(x)*sqrt((m+x)^2-1)*(x+sqrt((m+x)^2-1)));
IntegralA:=int(A,x=0..infinity);
P:=sqrt(x)/(sqrt((x+m)^2-1)*(x+m+sqrt((x+m)^2-1)));
IntegralP:=int(P,x=0..infinity);
f3:=(2*(-beta*Omega*m/sqrt(2))-delta)*beta+Omega/sqrt(2)*(alpha^2+(3*(beta*Omega)^(3/2)*int(A, x = 0 .. infinity))/(4*2^(3/4)));
f4:=alpha^2+beta^2+3*(beta*Omega)^(3/2)*eval(IntegralP,m=1)/(4*2^(3/4))-1;
f3A:=algsubs(beta=-sqrt(2)*mu/(Omega*m),f3);
f4A:=algsubs(beta=-sqrt(2)*mu/(Omega*m),f4);

_EnvExplicit:=true:
solve({f3A,f4A},[alpha,mu]);

Also, note that Maple can't figure out that

 MeijerG([[-1, -1/2, -1/2], []],[[-1, -1], [-2]],1) = 4*Pi

Using that, the equations above can be simplified.

Alec

In Maple, numbers are complex by default, and logarithms for negative numbers are defined as log(-n)=log(n)+Pi*I.

with(RealDomain);

would give logarithms of absolute values (but you'll see some other weird things instead.)

Alec

floor.

For nonnegative numbers, also trunc can be used, but it works differently for negative numbers.

Alec

Edwin,

There are some weird things that could be done with diacritical marks palette, such as typing u, then Ctrl+Shift+" and then the umlaut sign, but that seems to work only in math mode, and even there put diacritical marks too high. Some similar things were discussed in the xhat thread.

Alec

It is easy to do using display command,

with(plots):
a:=plot(x^2,x=-1..1):
b:=plot(x,x=-2..2):
display(a,b);

Alec

Roman Extended Lower Case palette also can be used. In the math mode it also can be entered as uum Ctrl+Space .

Alec

Maple still can be used to obtain the answer. For example, as

Digits:=15:
evalf(mul(1+1/ithprime(k)^4, k=1..5000)):
identify(%);
                                 105
                                 ---
                                   4
                                 Pi

Alec

I also get an interesting info message:

product:   "Cannot show that 1+1/ithprime(k)^4 is continuous on [1,infinity]"

Alec

PS "at least it is as strong as Euler" seems to be at a similar level though -Alec

In Maple, using u[t] means that u is something that can be indexed - a table, an array, or a list, for example.  Plus, you can't use dependent variables in collect - u and u[t] - even if u is a list, because the answer is not uniquely determined in such cases. It works OK in other examples because there is no such a contradiction there.

Still, it is possible to get the answer that you would like to see using collect as

collect( u*(u[t]+1),u[t]);

                              u u[t] + u

A normal way of doing that would be

expand(u*(u[t]+1));
                              u u[t] + u

Producing such an error message still may be considered as a bug. Some functions used in collect, such as `collect/coeffs` seem to be quite outdated, and use deprecated procedures and variables.

Alec

Something like that can be done as

`&/`(`&*`(x1,x1),`&+`(x1,x1));

                       (x1 &* x1) &/ (x1 &+ x1)

Alec

The more or less standard way is to use evalf/Int. Somehing like

core1 := (t0,t1,a,b,g,d,eps)->
evalf(Int(h(u,a,b,g,d), u=2*t0/(d*g)..2*t1/(d*g),epsilon=eps)):

core1(.5, 2.1, .5, 3, 3.14, 2.4, 10^(-32));
 1.636668036549567312072601247206393398244078914859354065223268055

It is interesting that the answer is different than in Axel Vogt's post above.

Another bug related to this is

Digits:=10:
core2 := (t0,t1,a,b,g,d,dig)->
evalf(Int(h(u,a,b,g,d), u=2*t0/(d*g)..2*t1/(d*g),digits=dig)):

core2(.5, 2.1, .5, 3, 3.14, 2.4, 6);
                                       14
                            0.304448 10

(But I am not submitting the SCR.)

Alec

For standard product (with weight 1), one can do the following, for example,

e:=Vector(4,i->x^(i-1)*exp(-x^2/2)):
`&*`:=(a,b)->int(a*b,x=-infinity..infinity):
G:=Matrix(4,(i,j)->e[i]&*e[j]):
L:=LinearAlgebra:-LUDecomposition(G,method='Cholesky'):
f:=L^(-1).e;

To check it, notice first that L^(-1) is low triangular, and second, that

F:=Matrix(4,(i,j)->f[i]&*f[j]);

is the identity matrix.

There are many other ways...

Alec

And submit it to Maple wiki, so that other people also could use it if they wish.

Alec

I just plot it,

plot(eval(f,[t=x*h/tau]),x=-20..20);

with f being the left hand side of your equation minus the right hand side of it, and it looks as if it doesn't have real solutions. Are you interested in complex solutions?

Alec

See my blog posts, Accessing Magma from Maple and Search Pi.

Alec