WP 34S --> WP 31S

[Manolo Sobrino]

(04-13-2014 10:03 AM)Paul Dale Wrote:  But x! isn't implemented recursively except in beginners' guides to programming languages. The 34S can do sequential multiplications for integers but in generally uses the LnGamma function instead.


- Pauli

Now we are nitpicking again... "just too cool in a recursive way of multiplications" was never meant to be a formal statement. I like the idea of having x! under multiplication because for integers that's what it is. But I said before that: "it really should be this one, %CH on an arithmetic, x! with the transcendentals". If I say transcendentals it's because I know what a transcendental function is, something that a product of positive integers is not. Do we really have to type the representation of n!: $$n!=\int_0^\infty t^n e^{-t} dt$$ which holds (n+1)! = (n+1) · n!, and can be extended to $$\Pi (x)\equiv\int_0^\infty t^x e^{-t} dt$$ over Reals, in terms of which the Gamma Function is defined as $$\Gamma(x)\equiv\Pi (x-1)$$, and is easily proved that $$\Gamma(x+1)=x\:\Gamma(x)$$, for whose non integer or non simple rational values you can for instance grab your copy of Abramowitz to get accurate to some extent, albeit old, approximations to begin with? Do we all know that stuff, don't we?