Works for concrete i

Markiyan Hirnyk — Wed, 06 Feb 2013 19:14:13 Z

A way

Preben Alsholm — Wed, 06 Feb 2013 19:39:33 Z

restart;
with(inttrans):
#r := sqrt(2*p)*exp(p*t)/(i-1)!*Diff((t^(i-1))*exp(-2*p*t),t$(i-1));
#Since i-1 might be 0 we shall use this version:
r := sqrt(2*p)*exp(p*t)/(i-1)!*Diff((t^(i-1))*exp(-2*p*t),[t$(i-1)]);
L := laplace(r,t,s) assuming i::posint;
Ld:=convert(L,diff);
Ld; #Gives a surprising error (but see below)
#So we do a little work by ourselves:
Diff((t^(i-1))*exp(-2*p*t),[t$(i-2-k)]); #Using k for _U1
value(%) assuming k::nonnegint,i::posint;
eval(%,t=0);
value(%);
#Since we have that the powers of t involved are greater than 0 this result is correct.
#So the laplace transform is
L1:=eval(L,sum=0);
#Doing a check for i = 1:
eval(r,i=1);
laplace(value(%),t,s);
eval(L1,i=1);
#OK

#Workaround for the problem mentioned above:
LS:=subs(sum=Sum,L);
Ld:=convert(LS,diff);
value(%);

Addition

Markiyan Hirnyk — Wed, 06 Feb 2013 19:21:38 Z

See the output of

Download r1.mw

By hand

Markiyan Hirnyk — Wed, 06 Feb 2013 20:34:23 Z

This is made by hand

L1:=eval(L,sum=0); .

MaplePrimes - answers and comments on Question, how to laplace transform this

Works for concrete i

A way

Addition

By hand