I on solving ∫e^(z^2)* fn(z) dz, where fn(z) =. .

[T.Engineer]

I need to work on solving ∫e^(z^2)* fn(z) dz.

where fn(z) = d^n/dz^n * e^(-z^2).

Thanks alot!

 

[cliowa]

I need to work on solving ∫e^(z^2)* fn(z) dz.

where fn(z) = d^n/dz^n * e^(-z^2).

Thanks alot!

Try working out (inductively) the form of fn(z).

 

[T.Engineer]

Try working out (inductively) the form of fn(z).

you mean to find the derivative for the
fn(z) = d^n/dz^n * e^(-z^2).

and then substitue it?

 

[cliowa]

you mean to find the derivative for the
fn(z) = d^n/dz^n * e^(-z^2).

and then substitue it?

Indeed, yes. Try f1, then f2 and so on to see what's going on.

 

[T.Engineer]

Indeed, yes. Try f1, then f2 and so on to see what's going on.

the derivative for e^-(Z^2) is
-2 Z e^-(z^2)

is not that true?

 

[cliowa]

the derivative for e^-(Z^2) is
-2 Z e^-(z^2)

is not that true?

Yes it is. Do you notice anything special about the integral?

 

[T.Engineer]

Yes it is. Do you notice anything special about the integral?

Now if I will substitute the derivative of fn(z)
Which is:
-2 z * e^(-z^2)
So, the integral equation will be like this:
-2 z * e^(z^2) * e^(-z^2) dz
here I get confused and I couldn’t find the integral?

 

[cliowa]

Now if I will substitute the derivative of fn(z)
Which is:
-2 z * e^(-z^2)
So, the integral equation will be like this:
-2 z * e^(z^2) * e^(-z^2) dz
here I get confused and I couldn’t find the integral?

What is e^{a}\cdot e^{b} equal to?

 

[T.Engineer]

What is e^{a}\cdot e^{b} equal to?

you mean it will be somthing like this
e^[(z^2)*(-z^2)]

or it maybe e^(a+b)

 

[cliowa]

you mean it will be somthing like this
e^[(z^2)*(-z^2)]

or it maybe e^(a+b)

There's no guessing involved there! It's e^a*e^b=e^{a+b}.

 

[T.Engineer]

There's no guessing involved there! It's e^a*e^b=e^{a+b}.

So, the integral it will be like this:
-2 Z dz

is not that right?

 

[cliowa]

So, the integral it will be like this:
-2 Z dz

is not that right?

That's correct.

 

[T.Engineer]

That's correct.

Thanks alot!