ComputerUser

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These are questions asked by ComputerUser

f1 = u1*f1 + u2*f2

f2 = u3*f1 + u4*f2

 

1. obviously u1 = 1 and u2 = 0 is solution, would like to see an exmaple which exist other solution?

2.

can it be seen as an matrix question such that matrix A := [u1, u2; u3, u4;];

or i should see them separately f1 = u1*f1 + u2*f2 and f2 = u3*f1 + u4*f2 ?

which Maple function calculate this?

3.

if want to determine whether [g1, g2] is member of [f1, f2], u1 = 1 and u2 = 0 can not be solution?...

http://wenku.baidu.com/view/7d013c8c680203d8ce2f24ee.html

 goal is to evalute to (5.10)

restart;
with(inttrans):
with(SumTools):
r := sqrt(2*p)*exp(p*t)/(i-1)!*Diff((t^(i-1))*exp(-2*p*t),t$(i-1));
L := laplace(r,t,s);
L := int(r*exp(-s*t), t=0..infinity);

no matter laplace it or integrate it, also failed

when doing ztransform

restart;
with(inttrans):
with(SumTools):
network := sqrt(2*p)*((s-p)^(i-1))/((s+p)^i)
ztrans(network, s, z);

error, recursive

http://en.wikipedia.org/wiki/Laguerre_polynomials

http://wenku.baidu.com/view/7d013c8c680203d8ce2f24ee.html  

how to evaluate to equation (5.9) in page 195 from rodrigues formula?

rodrigues := exp(x)*(x^alpha)/n!*Diff(exp(-x)*(x^(n+alpha)), x$n);
rodrigues := subs(x=2*p, rodrigues);
rodrigues := subs(alpha=1/2, rodrigues);

Laguerre
charc := -(-1/(-1+I*X))^alpha/(-1+I*X);
Density := int(-exp(-I*X*u)*(-1/(-1+I*X))^alpha/(-1+I*X), X = -infinity .. infinity);
can not evaluate

Meixner
charc := (1+mean/(-1+exp(I*X)*mean)-mean*exp(I*X)/(-1+exp(I*X)*mean))^gamma;
Density := int(exp(-I*X*u)*(1+mean/(-1+exp(I*X)*mean)-mean*exp(I*X)/(-1+exp(I*X)*mean))^gamma, X = -infinity .. infinity);

Bernoulli
charc := 1/(I*X/(-1+exp(I*X)))^n;
Density := int(exp(-I*X*u)/(I*X/(-1+exp(I*X)))^n, X = -infinity .. infinity);...

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