The Natural Logarithm and its Series Expansion - 2 Ways [ ln(x+1) at 0 ]

[@tatjanagobold2810]

Flammy, this day was quite shitty for me due to terrible recurring migraines, but this video lifted me out of bed because I just love series expansions and all your videos in general

[@luchisevera1808]

Why do they call it a natural log if there are no trees to be seen? HmMmMmM...

[@69erthx1138]

Because it's unnaturally derived by inverting the Napier series?

[@remlatzargonix1329]

Luchi Severa .....it used to be called the Napierian log, more commonly than the natural log, but now, it seems the other way around.

[@sichel94sam]

I usually watch these because youre th meme Lord but this time it helped me actually, thank you for being so amazing papa flammy 😍

[@SuperMiketron]

Finally a video I can understand myself and not feel like a dumbass. Thanks papa!

[@officialEricBG]

We literally did this in lectures today, the lecturer had the old way in his notes but he also just went your way :D

[@hotlinkster123]

We did it today too, exactly the same. Could we be in the same university??

[@abdullasulfikkar5282]

I just don't know what to comment 😂😂😂😂😂😂 .Keep it flaming

[@abdullasulfikkar5282]

@@PapaFlammy69
❤❤❤❤

[@atrimandal4324]

Another series expansion! Thanks papa❤️

[@nontrivialdog]

I just used this to obtain the perturbative expansion of the free energy of a weakly interacting fermi gas!

[@nontrivialdog]

Finding the series is simple if you notice that f'(-x) is the geometric series!

[@nontrivialdog]

Oh nvm you covered that too! Sorry for doubting you papa flammy!

[@remlatzargonix1329]

nontrivial dawg ...I usually just use antacids, and then the gas subsequently goes away....

[@danielescotece7144]

How about a series on sigma-algebras?

[@korayacar1444]

1:29
It‘s the negative _first_ power, if you‘re curious.
edit: timestamp

[@willnewman9783]

Why are you indexing over prime ideals?

[@abdussalim3661]

good boi

[@tobiasguivarch4537]

I think you missed to put the minus sign in front of the sum symbol on the thumbnail...

[@amadeuszsitnicki3433]

the thumbnail is actually incorrect

[@PapaFlammy69]

oh ye, p+1th power!

[@okoyoso]

That reminds me. Any progress on that lnx = f(x) + lnf(x) problem?

[@okoyoso]

@@PapaFlammy69 Maybe I'll post it on the sub

[@tytuer]

Logarithm function annoys me. It has no power series that converges for real numbers,( if there is, I do not know) also, I could not find such a function f(x), that is not a logarithm and satisfies lim(x->inf)f(x)=inf and lim(x->inf)(f(x)/lnx)=0.
Why do I bother myself with these? I am just an engineer. Let's take π=3. Lolz

[@MurtadhaAljanabi]

Can't we just use uniform convergence of power series to justify interchanging the sum and the integral?

[@압둘하미드이드리스]

Good

[@thiagosalatino1302]

Queria te mandar um problema (._.

[@muneebahmad7729]

🖤🖤🖤🖤💥❤️

[@josueantonio2123]

How to Integrate ( x^2sec^4(x) ) ???
Help pls!!

[@attepiltonen6607]

your f looks more like a rho lmao