Question

Question about Legendre

Answer 1

Legendre polynomial or theorm ?!

Answer 2

or legendre formula

Answer 3

exactly or about Legendre himself ?
like history ?

Answer 4

i am familiar only legendre formula though. whats a legendre polynomial @ikram002p

Answer 5

someone asked a question on linear combinations of the first five legendre polynomials earlier

Answer 6

its sort of polynomial of contour integral

Answer 7

\[\large P_n(x) = \dfrac{1}{2\pi i} \oint (1-2tx+t^2)^{-1/2}t^{-n-1}dt\]

Answer 8

i might need a refresher online or something

Answer 9

i never took complex analysis before, so idk how to work above integral

Answer 10

hehehe convert it into some sum , this will do it
http://prntscr.com/4jj86t

Answer 11

sorry i think it was the legendre polynomial with roots a,b,...

Answer 12

whats exatly ur question ?

Answer 13

sorry i was just doing research

Answer 14

i should have stated that in the question

Answer 15

i want to know more about Legendre polynomials

Answer 16

pick your brain about Legendre stuff

Answer 17

\[\large \begin{align} \\ P_n(x) &= \dfrac{1}{2^n} \sum\limits_{k=0}^n \binom{n}{k}^2 (x-1)^{n-k}(x+1)^k \\~\\ P_0(x) &= 1 \\~\\ P_1(x) &= x \\~\\ P_2(x) &= \frac{1}{2}(3x^2-1) \\~\\ &\cdots
\end{align}\]

Answer 18

where are they used?

Answer 19

yes

Answer 20

idk where they used , i only learned it in contour integral >.<

Answer 21

can you remind me what a contour angle is

Answer 22

contour integral , is an integral that you convert real integral to complex , then take branch cuts , find a series that express that function then integral would equal sum of residues at the branch cuts