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19 years, 286 days

solving quartic equation...

k^4-k^2*(4*u*m+2*q^2)+k*(8*m*E*q)+4*m^2*(D^2-e^2+(q^2/2*m-u)^2)=0;
solve(%,k);
convert(%,radical);

The result is about 10,000 characters long, so probably not of much use to you...

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G A Edgar

Let G(x) denote the no. of ways of repre...

Perhaps there is some connection between x and n ?

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G A Edgar

really?...

Another remark: Do you really need the determinant?  Or would some other calculation suffice?

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G A Edgar

Assignment in Maple is := Maybe you wan...

Assignment in Maple is :=

Maybe you want to do something like this...

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G A Edgar

Probably you should also say what OS you...

Probably you should also say what OS you are going to use to run it.  On my Mac, Maple versions prior to 9 won't run in MacOS 10.8, for example.

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G A Edgar

guess...

I'm guessing it is this...

Int(Int(u*v/sqrt(2*Pi)*(1/2+1/2*erf(1/2*sqrt(2)*u))*(1/2-1/2*erf(1/2*sqrt(2)*v))*exp(-(u^2+v^2)/2),u=-infinity..v),v=-infinity..infinity);

General advice: for evaluation of multiple integral, try Student[MultivariateCalculus][MultiInt]

I get  (1/24)*2^(1/2)*(-3+2*3^(1/2))/Pi^(1/2)  for this ...

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G A Edgar

possibility...

A possibility.

Sum of the geometric series sum(x^b,b=0..a-1) comes out as (x^a-1)/(x-1) according to Maple .  Which is almost right: it is right except when x=1 .  Now your sum

sum(cos((2*Pi*b*12)/(a)),b=0..a-1)

is real part of geometric series

sum(exp((I*2*Pi*b*x)/(a)),b=0..a-1)

so Maple computes it as zero.  That is correct unless exp(2*Pi*x/a) is 1.  So assigning 0 for this symbolic sum is the best Maple knows how to do.

With "add" we tell Maple not to try a symbolic sum, just add the items (but to do that we cannot have symbolic upper limit a-1 unevaluated).

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G A Edgar

round-off...

shouldn't evalf(a) and evalf(b) give exact same result?

Yes, they are the same (up to round-off error).  Try Digits:=50 first, then do these evalf's, and see what you get.

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G A Edgar

1D...

Here it is in 1D Maple input format:

```u:=int(-4*(16*c+3)*exp(-1/(2)*sqrt(-16*c-3*Zeta))
/(64*exp(-sqrt(-16*c-3*Zeta))+256*c*exp(-sqrt(-16*c-3*Zeta))
+8*exp(-1/(2)*sqrt(-16*c-3*Zeta)) +1),
Zeta);```
`But "don't use 2D input" is not a very good reply to the OP... Someone`
`who uses 2D input should help him out (I don't).`
` `

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G A Edgar

special case...

First do the simplest special case, c=1, n=1 ...

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G A Edgar

common sense...

Yes,  the line through the two points  A(1, 1) and B(1, -2*m + 2) is a vertical line, so it does not have an equation of the form y=k*x+q ... What do you want in that case?

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G A Edgar

according to maple...

according to Maple...

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G A Edgar

Use `...` or "..." for strings inside th...

Use `...` or "..." for strings inside the cat.  Also, you may need to substitute k into lf[k] before you make it into a string ?

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G A Edgar

You can also use "surd" for real-valued ...

You can also use "surd" for real-valued odd roots.  See ?surd

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G A Edgar

Is there some relation between f and F ?...

Is there some relation between f and F ?  In F"(n)(s) is that the second derivative with respect to s ?

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G A Edgar

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