The Legendre Polynomials in Closed Form

#mikethemathematician, #profdabkowski, #mikedabkowski

[skapun]

Been loving the content lately, keep it up!

[holyshit]

I tried to do this from generating function but once I applied binomial expansion twice I had got n+k as powers of t not just n
and people from math forums wasn't very helpful as usually

From solution of ordinary differential equation I had got sum to calculate
Woudn't be better to have recurston backward
I went backward but expressed a_{n-2k} in terms of product
Then from y(1)=1 I had got sum to calculate a_{n}