# Laplace transform and HP50g

1. Aug 8, 2011

1. The problem statement, all variables and given/known data
Hi, I am writing a little program (I need it for my course from Theory of Reliability) and as I am neither experienced mathematician nor programmer I faced with this problem.

What would this formula

Look like if I would sole it for 'z' not for 'Fz' ?

2. Relevant equations

Right now equation in my HP50g (I managed to do that) for solving for Fz looks like:
\<<
"Enter z" "" INPUT STR\->
\-> z

'Fz=1./\v/(2.*\pi)*\.S(0.,z,EXP(-(1./2.)*z^2.),z)'

"F(z)"
\->TAG
\>>

Thank you in advance,

Regards,

2. Aug 8, 2011

### MisterX

That does not seem like a Laplace transform to me.

Anyway, to solve for $-\frac{1}{2}z^{2}$, you could multiply both sides by $\sqrt{2 \pi}$, apply the fundamental theorem of calculus, and then apply the natural logarithm to both sides.

3. Aug 8, 2011

### Ray Vickson

Your notation is bad and your question is not well stated. I assume you are defining the function F(z) = int[exp(-t^2 /2) dt: t= 0..z]/sqrt(2pi), and you want to solve the equation F(z) = p; that is, you want to find which value of z. Is that your question? There is no exact, finite expression for F(z) or it's inverse. You need to use numerical methods and/or approximations.

RGV