Mod-04 Lec-10 Analytic continuation and the gamma function (Part II)

[@peterpalumbo1963]

I am familiar with the Gamma Function but not at this level. You present much food for thought.

[@PrinceVishwakarma-t1o]

great lecture sir ji... thank you so much

[@MarkusJaeger-itguy]

always the sign of a great professor when the equations are derived live right there on the board instead of being read to you

[@bboyHarrypotter]

Well technically he read the Weierstrass product representation of the gamma function at 23:36, without derivation (both in this lecture and in the lecture notes).

[@knivesoutcatchdamouse2137]

@@bboyHarrypotter Yeah, I am loving these lectures, but I do wish he had demonstrated the derivation of the Weierstrass Product for Gamma (although I'm already familiar with the method), since it has some relevance to the gamma constant and is also just interesting, not to mention the representation of Gamma function as a limit of a sequence of products Gamma_n with n^x in the numerator and then x * [(1 + x/1) (1 + x/2) ... (1 + x/n)] in the denominator.

[@SetsukoSeita123]

It's Duplication formula for gamma function. Doubling and duplication can be so confusing, though! Great lecture, as always.

[@rahmatkhan3982]

very helpful lectures

[@akarshnarasimhan]

Does anyone know what is a good reference for these things? I've seen the standard references like Ahlfors and they contain a lot of this material, but I'm wondering if there is a book that's more example-heavy like Prof. Balakrishnan.

[@hbatmit]

www.amazon.com/Mathematical-Physics-Applications-Problems-Solutions/dp/9386761114/ref=sr_1_2?crid=VFJ2INKNRQKM&keywords=mathematical+physics+with+applications%2C+problems+and+solutions&qid=1556504380&s=gateway&sprefix=mathematical+physics%2Caps%2C140&sr=8-2

[@anuvansh1828]

Is there any reference book for this topic? specially on special functions in complex analysis

[@bboyHarrypotter]

11:42 He looked at his notes! He is a human!

[@JONASACHUOBIMaths]

please i need the lecture notes

[@KishorBharti1]

I think the integral @ 6:06.( Gaussian ) should have an extra half in front of it.

[@akarshnarasimhan]

You are right, I think too. The integral going from -infty to +infty has no factor of half, but 0 to infty should have it.

[@HariprashadRavikumar]

yes

[@pinakichatterjee705]

In Poisson's trick x and y need to go -inf to +inf in order to cover whole 2D plane. You're right, it misses a factor of half. That aside, somebody commented this 8 yrs ago, it's not common these days for a lecture series to survive a decade. Bulky is the greatest

[@NilodeRoock]

Why does this professor put dt immediately after the integral sign, I have never seen this before? - Worse: why is he fiddling sequences at 08:35 ? Is the man dialectical ?

[@NilodeRoock]

He does not seem to understand the difference between Ln, log and Log. 12:04

[@chamidumadumal7130]

Shut up.