maclaurin series of e^(e^x) in terms of x

[latent pagoda]

Can someone explain how to evaluate this in terms of x?

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[latent pagoda]

@helper

[subtle mist]

You can evaluate it as a double series

Like $e^{e^x}=\sum_{n=0}^{\infty} \frac{e^{nx}}{n!}$

[latent pagoda]

Like this?

[astral sorrel]

Rotor

[latent pagoda]

If I’m only doing up to x^2

[subtle mist]

Wdym ?

[latent pagoda]

Finding the series up to the coefficient of x^2

[subtle mist]

Are you doing a Taylor expansion like e^x=1+x+x^2/2 + o(x^2)?

[latent pagoda]

Yeah

[subtle mist]

Ohh I see

[latent pagoda]

That’s what I did

[subtle mist]

If you are doing till second order then that’s correct

[latent pagoda]

Okay perfect

Was just doing it for understanding

[subtle mist]

Don’t forget that the terms of power >2 are négligeable and you can also use Taylor young’s formula

It’s another possibility

[latent pagoda]

I don’t know that

It’s not in my specification of learning

[subtle mist]

Ok no problem

[latent pagoda]

But thank you for the help

[final matrix]

i feel like this is harder than just taking the derivative

[latent pagoda]

I know but the question says I have to do it that way

Hold on

[final matrix]

interesting

[subtle mist]

well you said yourself Taylor you isn’t possible

*Taylor young

[final matrix]

this is also the bell numbers EGF

[latent pagoda]

Sorry you’re gonna have to explain 😭

[final matrix]

not too relevant, just happens that a certain sequence bn which counts number of set partitions, appears here

[subtle mist]

Isnt it like the generator function or something ? Can’t remember

[dull snow]

2023 core pure 2

@latent pagoda I think that’s right

The “x+1/2 x^2 + 1/6 x^3” becomes ur “x”

U sub that into the maclaurin expansion

Neglecting all the terms higher than x^3 of course

[zealous stream]

ib math ahhh

[latent pagoda]

Nah