a0 = 1.5; a1 = 0.4; b1 = 0.3; g1= 0.7
nu = rep(0,1)
h.new = rep(0,1)
ddp = rep(0,1)

nu[1]=0

h.new[1] = a0/(1-a1-b1)
ddp[1] = 0.5*log(g1)- g1*h.new[1] +
  nu[1]*(log(nu[1])-1) - log(factorial(nu[1]))+(g1)*nu[1]*
  (1+log(h.new[1]/nu[1]))

###> ddp
###[1] NaN

###h.new = 1.5/(1-0.4-0.3) = 5

###ddp
###= 0.5*log(0.7)- (0.7)*(5) +
###(0)*(log(0)-1) - log(0!)+(0.7)*(0)*
###(1+log(5/0))

###= 0.5*log(0.7)- (0.7)*(5)

###= -0.528333

term3 <- if (nu==0) 0 else 0*(log(0)-1)
term5 <- if (nu==0) 0 else g1*nu*(1+log(h.new/nu))
ddp = 0.5*log(g1)-
    g1*h.new +
    term3 -
    log(factorial(nu))+
    term5