Legendre's ODE II: Deriving a formula for Legendre Polynomials

This video is a continuation to my 1st video on Legendre's differential equation. Here, I derive a formula for the coefficients of the Legendre polynomials using the recursion relation found in the last video.

Questions? Ask me in the comments!

[omarchikhar]

Please continue your videos! I'm a physics and CS major and I always come to this channel when I don't understand something from my courses! This channel is very useful!

[rishavsinha]

you saved my life..
a physics major knows.. how much hectic it is to differentiate to recieve polynomials.. 😢😢

[padmajagunda]

Thank you for your lectures and your way of explaining things.

[avinashyadav]

It's sad to see so much less views on such a video. Your work is really awesome man, you just saved my sem.

[karimmohie]

Super precise! Amazingly condensed in a professional way!

[Abhishekgupta-hnhz]

Saved my day. Thanks for making such helpful videos

[abdsalmansalman]

i dont know to express of my feeling really thank you very much

[alxanderjon]

probably a silly question, but in the beginning of the video when you defined the a_k value you made sure to choose a value related to the k constant in the legendre equation, and you made sure to point out that this k shouldn't be confused with the running summation. Yet when you did the change of index you used k for the running sum and used this running sum k to cancel with the constant k terms. What is the insight I am missing here? It feels like these should be two different values unable to cancel with each other

[ronpearson]

So awesome, I am excited to understanding Dyadic Greens functions so I can see how wave guides are sized.

[tjk]

3:51 But..., where it comes from? How do you know, that this actually works?

[adityasahare]

There is a mistake on 6:28 of video. (K-2)! in the denominator Was supposed to be to the power 2. What about that?

[shubhampandit]

I think the recurrence relation is a_n+2 = - ((n-k)(n+k+1) / [ (n+2)(n+1) ] ) a_n. I guess you drop the minus sign. By the way, You made a great video. It really helped me a lot.

[qirunwei]

Hi! Thanks for the great explanation. Using your videos to learn maths for second year physics. I was wondering, how did you arrive at the expression for ak in the red cloud? I couldn't find it given anywhere in the preceding working.

[zhongyuanchen]

Is the final solution in this video that is a finite series really equal to our sollution? I mean, even if we use the recursion relation backward to go from the highest order to the lowest, hence we get a finite series, the recursion relation itself still indicates that there are more terms that are higher than the highest order that we chose.  In a previous video, you said that either odd or even will terminate but not both.  Can using the recursion relation backward really change a infinite series into a finite series? Can we really use an equal sign?

[Legend_Hunter_Original]

Hey man amazing video, quick question though, how do we actually show that P(x=1) =1? I mean i plug it in the final eqn and we are only left with is a_(k-2m)... and the only conclusion is that it must equal 1. But how do we show that a_(k-2m) summed over m is 1? does it simplify to a known series or...? thanks

[AliJoohy]

Thanks for the tutorials, could you please tell me what program do you use to write such beautiful lectures.

[m_e-fq]

hi.what is the radius of convergence legendre university ask us to tell them how we find can i tell them???they told us us a(n+2)

[satyamkumar]

Please sir, make video on leguerre and hermite differential equation

[鍾凱凱-yc]

why the 2:01 recursion relation is terminate at x^k, I know that the recursion relation have n-k so n = k wil terminate the part of k is odd or even, and another part of even and odd will not terminate?
how to explain? thx

[鍾凱凱-yc]

The infinite series solution is when k is odd the even series does not terminate part, k is even when odd series does not terminate?