The Dirichlet integral: integral of sinx/x from -ve to +ve infinity using contour integration

[@zunaidparker]

14:40 Int(cosx/x)=0 only applies if you accept the Cauchy Principle Value. Strictly speaking the integral doesn't converge. Great video! Happy New Year!🎉

[@maths_505]

Happy new year mate🥳 And we all know that Cauchy is top G so why not take his principle value 😂😂😂

[@osaether]

Great video! I am an 59 year old electrical engineer (MSc) and study complex analysis in my spare time :-)

[@williammartin4416]

Can you provide a link to the "Myers Solution" that you referred to

[@lakshaygupta5683]

happy new year dude!

[@maths_505]

Happy new year mate

[@justafanofalphabetlore]

I like complex analysis with you ❤❤❤

[@donaldlee8249]

An alternative way to look at the small bump over 0 is using Cauchy’s integration theorem as it just traversed half a circle in the opposite direction

[@thomasblackwell9507]

Happy New Year to you all! I wish you health, wealth and happiness!

[@maths_505]

You too my friend

[@manstuckinabox3679]

Is this a celebration for my 94.25% (yes, the final test didn't really affect the overall grade) on my complex analysis course? we've gone far enough into the complex feild, might as well become quaternion men, which begs the question, is there an extrapolation from single variable complex function contour integration to quaternion-type functions? like some sort of double contour integration? are the same theories as cauchy's integral formula, or a laurent type expansion applicable to these "objects" the matter really interest me even got a book about "hyper"-complex numbers, I'll begin with it about next month lol! but it's such an interesting subject to explore! AND HAPPY FREAKING NEW YEAR! one of the greatest moments of this year, and I'm not saying this just to make you blush, is finding your channel, such a cozy place to get the most intuitive explanation to those dirty integrals!

[@maths_505]

Happy new year my friend Thank you so much for the support!

[@pixel0818]

why do your z's look like deltas and 3s??

[@yoylecake313]

What do you app do you use to write?

[@alphasuthamedia]

I have a question. You have gamma and little gamma. When your big gamma goes to 0 using modulus properties. Then why your little gamma is evaluated only using lemma, is it also true if using modulus properties😅, if so, the little gamma turns to integral of abs(ie^iɛe^iΦ) dΦ, not only its is so hard to evaluate it (not just with plugging ɛ=0🥲) but how to evaluate integral with modulus function 😂. Realizing that Im just starting to following some contour integration things (mainly your channel) since a week ago, it is true im still dumb 😂. Btw amazing video. Keep it up.

[@justafanofalphabetlore]

Almost 2023

[@douglasstrother6584]

Nothing says "Happy New Year" like a little Number Theory! The prime factorization of 2023 = 7 * 17 * 17. It *might* come in handy.

[@justafanofalphabetlore]

@@douglasstrother6584 i know this. The rule to decompose 2023 into prime numbers

[@justafanofalphabetlore]

I invented an unfailable trick for n/7: take 1001 and substrate the number of thousands to number of unity.

[@justafanofalphabetlore]

It works at each time ! Enjoy

[@konchady1]

Great video. However, you need to take care at 0. This function is called the sinc function if you define the value at 0 to be 1. With cos(x)/x, the problem is that it diverges at 0. So it is wrong to say that the integral is 0. Even in the residue proof, you skirt around 0. Adequate care must be taken to ensure that integrals make sense.

[@maths_505]

Yes in the strict sense the cosine integral does not converge. It's the PV that is zero.

[@nazmurrahmannobel11]

Bro, according to my understanding,you have proved that principle value of int(sin x/x)=1

[@thomasblackwell9507]

Homer Simpson would be proud of your drawing!

[@maths_505]

Best comment I've read all day

[@thomasblackwell9507]

@@maths_505 Glad you enjoyed it. We aim to please. HHMMM, donuts 🍩!

[@marcrindermann9482]

wasn't Jordan German despite his French name? edit: never mind, was a different Jordan 😆

[@johnsantavicca5016]

No Thank You

[@maths_505]

Wth 😂 Not a fan of contour integration?

[@johnsantavicca5016]

@@maths_505 no. I thought it was about colon cancer. I can't answer. I do love smart ppl though.