this video is really great and i like how u make things simple and i am looking for your up coming videos specially the wallis product i finally feel like i understand the gamma function thanks alot
Pre-watch question: why would you need an infinite product for the gamma function when it itself is defined as a finite product? Will watch later and see.
That’s a great question. The idea is to find a way of extending the definition of the factorial to include numbers other than positive integers. For example, what would (1/2)! equal? As this video demonstrates, redefining the factorial (and gamma function, which is very closely related to it) as the limit that results when we take an infinite product allows us to recover the factorial values we expect for positive integers but also provides a way to define the factorial on positive (and negative!) fractions.
this video is really great and i like how u make things simple and i am looking for your up coming videos specially the wallis product
i finally feel like i understand the gamma function thanks alot
It is my pleasure. Thank you for the supportive feedback!
Pre-watch question: why would you need an infinite product for the gamma function when it itself is defined as a finite product? Will watch later and see.
That’s a great question. The idea is to find a way of extending the definition of the factorial to include numbers other than positive integers. For example, what would (1/2)! equal? As this video demonstrates, redefining the factorial (and gamma function, which is very closely related to it) as the limit that results when we take an infinite product allows us to recover the factorial values we expect for positive integers but also provides a way to define the factorial on positive (and negative!) fractions.