expand(convert(simplify(GammaDensity, size),exp)),size)

www.stat.rice.edu/~dobelman/textfiles/DistributionsHandbook.pdf

i use the derivation of gamma in above book to derive density again, but fail

GammaDist := int((lambda^k)*(z^(k-1))*(exp(-lambda*z))/(k-1)!, z=0..t);
GammaDensity := diff(GammaDist, t);

GammaDensity := (b^a)*(x^(a-1))*exp(-x*b)/GAMMA(a);

How to laplace transform for hypergeometric form in maple

if rsolve is solving difference equation for L(x) in summation(L*z^n, n=0..infinity)

can i use double encapsulation to solve for summation(L*z^n/n!, n=0..finity)

step 1 use rsolved result of a given classic difference equation times z^n/n! * t^n

step 2 then summation step 1 and use celine method to change into difference equation again

step 3 solve this new difference equation

then i imagine L should be L*z^n/n!

but i am not sure...

I use Hermit as example and try the following way, it can not sumtohyper,

how to get the hyper form from a differential equation?

restart;
with(gfun):
test4 := diff(P(x),x$2)-2*x*diff(P(x),x)+2*n*P(x)=0;
test4 := {diff(P(x),x$2)-2*x*diff(P(x),x)+2*n*P(x), P(0) = 1, (D(P))(0) = 1};
newtest4 := borel(test4, P(x), diffeq);
rec4 := diffeqtorec(newtest4, P(x), a(v));
rec4 := diffeqtorec(test4, P(x), a(v));
genfun := rsolve(rec4, a(v), 'genfunc'(z));