i am implementing q-Laplace

http://perso.uclouvain.be/alphonse.magnus/gbang/qbook712.pdf

when there are quite many differentiation rules

how to do a function for a new kind differentiation like a maple do?

1.

qRacah := qhyperterm([q^(-x), alpha*q^(-x)/(gamma*delta)], [alpha*q], q, gamma*delta*q^(x+1)*t, k)*qhyperterm([beta*delta*q^(x+1), gamma*q^(x+1)], [beta*q], q, q^(-x)*t, k);

i use inverse laplace to transform ordinary generating function into exponential generating function

can not further evaluated

2.

i do not know whether x is main variable or q is main variable or both are.

ff := eval(subs(x=0, exponential_genfun));

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