# Question:limit of the integral is function

## Question:limit of the integral is function

Maple

Hi

The integration in (F2) is not work properly.

My tyr is below:

restart:with(plots):
assume(d,real):

b:=-gamma1*tau0+I*tau0*Delta-2*a*(k-1)*xr:
a:=1+I*c;
c1:=sqrt(conjugate(a))/tau0:
c2:=0.5*((conjugate(b)/sqrt(conjugate(a)))):
lambda1:=2*(1-I*d)*(t-k1)/j+(1-I*d)^2:
lambda2:=t*(1-j)*k1/j+1/sqrt(2)*(1-I*d):
lambda3:=c1*(t-k1)/j+c1*(1-I*d)+c2:
J1:=sqrt(Pi)/sqrt(2)*(1-erf(lambda2)):
J1mod:=(Re(J1))^2+(Im(J1))^2:
g1:=0.5*sqrt(Pi)*tau0*exp(c2^2)*exp(-conjugate(a)*((k-1)*xr)^2)/(sqrt(conjugate(a))):

F2:=-sqrt(2)*int(exp(-x^2)*erf(sqrt(2)*c1*x+lambda3),x=-lambda2..infty);
Warning,  computation interrupted
J2:=sum(g1*J1+g1*F2,k=1..1);
J2mod:=(((Re(J2))^2+(Im(J2))^2)):
W:= unapply(no*J1mod+Omega^2*J2mod,d):
Omega:=0.01:no:=1:Delta:=0:tau0:=1:c:=0:gamma1:=0:j:=1:k1:=0:t:=2*Pi:xr:=1:
P1:=plot(W,-50..50,axes=boxed,title=tit,color=black,font=[2,3,18],thickness=2,tickmarks=[3,2],titlefont=[SYMBOL,14],font=[1,1,18],linestyle=1);

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