09/13/2014, 11:45 PM
(This post was last modified: 09/13/2014, 11:46 PM by sheldonison.)
(09/13/2014, 11:25 PM)tommy1729 Wrote:(09/13/2014, 07:15 PM)sheldonison Wrote: \( \exp(x)\sqrt{x} \approx \sum_{n=0}^{\infty} \frac{x^n}{\Gamma(n+0.5)}\;\; \) Have you seen this excellent asymptotic entire series?
Yes Ive seen this before.
Have you heard of hypergeometric functions or generalized hypergeometric functions ?
When I was still active at sci.math I mentioned the underrated and insuffiently known properties and powers of the hypergeometric functions and more particular their INVERSES.
Inverse hypergeometric functions is one those other " crazy math concepts " apart from tetration , collatz and prime twins.
Bill Dubuque and a few others recognized / remembered the power of these functions.
But its far from mainstraim.
It is amazing how unexpectedly these inverse hypergeometric functions can occur.
.....
A good understanding of the gamma function is essential.
Hey Tommy, I posted it on mathstack; http://math.stackexchange.com/questions/...237#930237 and got quick responses! I need to get really good at understanding and working with the Gamma function.
- Sheldon
