Maclaurin series of sin^2x

[@punditgi]

Prime Newtons is my prime source of math knowledge. Bravo, sir! 🎉😊

[@albajasadur2694]

We can also try to express sin^2(x) in terms of e^(i.2x) and e^(-i.2x). The Maclaurin series of the function e^(ix) is also well known.

[@jasonryan2545]

This was fun .... And literally a beautiful result. An equation that gives you what you need is nothing short of that word. Loved your explanation once again, Prime Newtons!

[@mariogomez8149]

I rarely comment on videos, but I have to say: The way you present these concepts is amazing!

[@yuyuvybz]

"I rarely comment on videos" is that supposed to make your comment of more quality that others? 😂😂😂

[@Abby-hi4sf]

So neat, the way you explain it. I wish all math students have a chance to view your channel! .

[@raymondseligman7003]

I find the analysis and explanations in this series just wonderful. While a PhD or advanced degree is certainly not a requirement to be smart and be able to get information across, it is very rare I think to find someone who apparently does not have those qualifications do such an incredible job. Where did you the scope of your knowledge of mathematics that you so clearly Express? Keep it up and don’t stop.

[@MathsScienceandHinduism]

As a maths educator and youtube creator, one of my fav channels to follow is Prime Newtons.

[@Abby-hi4sf]

You are the most gifted teacher! I was trying to find your older video of solving (x+7)^7= x^7 + 7^7 , to show it to the friend, it took me a while. If you put the equations on the title it is easy to find them easily in KZbin too.

[@joshdilworth3692]

How do you recommend a problem? I have one function I'd like you to look at that I've written that I think would be interesting to explore. Thank you for all of the maths that you do, and learning you facilitate!

[@stoqntoshev2817]

Can't we use that sin^2(x)=(1-cos(2x)/2 and the Maclaurin series for cos(x)?

[@nanamacapagal8342]

He does this in the second half of the video, at 11:01

[@stoqntoshev2817]

@@nanamacapagal8342 Sorry. I didn't watch the whole video.

[@Vega1447]

Why would anyone not use the double angle formula?

[@maxhagenauer24]

You could also just take the very simple maclaurin series for sin(x) and square it. So ( x - x^3/3! + x^5/5! - ... )^2.

[@Grecks75]

​@@maxhagenauer24But that expression is not a McLaurin series in itself as was asked for. In order to get one, you need to multiply the product of the two infinite sums out by folding the coefficients. That is not so easy!

[@johnnolen8338]

Very cool! 😎

[@ars7595]

Bro added life lesson for climatic end 😂

[@terryendicott2939]

Another way of doing this is to take the Maclaurin series for sin(x) and square that series.

[@abdullahbarish8204]

Thank you

[@RyanLewis-Johnson-wq6xs]

Maclaurin series of f(x)=2 x=(1-cos(2x))/2 sin

[@Dhruven-t2]

My dumbass would do (x-x³/3!+x⁵/5!)²😂

[@emanuellandeholm5657]

You can do that, but then you have to use the Cauchy product formula.

[@maxvangulik1988]

sin^2(x)=(1-cos(2x))/2 cos(x)=sum[n=0,♾️]((-1)^n•x^(2n)/(2n)!) cos(2x)=sum[n=0,♾️]((-4)^n•x^(2n)/(2n)!) sin^2(x)=sum[n=1,♾️]((-1)^(n+1)•2^(2n-1)•x^(2n)/(2n)!)

[@nanamacapagal8342]

that's what I would have done,just this time I would have combined the (-1)^(n+1) * 2^(2n-1) into 2 * (-4)^(n-1)

[@AlexSmith-dh1oz]

This was my first thought too