Pastelland Forum

dVanDaHorns wrote:You ain't going to learn transforms in AP Calculus. That's more of a university Calculus concept.
(I believe AP Calculus covers up to advanced differentiation and integration techniques, which is then reviewed in most first year calculus courses before delving into new material. Such as transforms. )

Yeah I know, that's what I meant.

dVanDaHorns wrote:As well, i'm not too sure what you are asking concerning the gamma function...if it's dealing with finding values for which the delta function will give you those fractions, it is definitely possible to do so using a numeric approach (i.e. using Matlab or MAPLE).
If you are inferring to expressing fractions as an infinite series of gamma functions, then I have no idea. It is probably possible, since any discontinuous function can be represented by a series of Heaviside functions, but once again, most likely a numeric approach using computers would be better.

Basically what I was wondering is if there is a simple (that is, in terms of 'well-known' constants like e, pi, the euler-mascheroni constant, etc.) representation of values like Γ(1/5). The gamma function is easily solved for integers as it corresponds to a shifted factorial, but no closed forms are known for any fractional arguments of Γ(z) besides half-integers. What I am wondering is if expressions representing these values that way even exist.

Taalit wrote:Basically what I was wondering is if there is a simple (that is, in terms of 'well-known' constants like e, pi, the euler-mascheroni constant, etc.) representation of values like Γ(1/5). The gamma function is easily solved for integers as it corresponds to a shifted factorial, but no closed forms are known for any fractional arguments of Γ(z) besides half-integers. What I am wondering is if expressions representing these values that way even exist.

Oh. Yeah, there haven't been any breakthroughs in that domain, just quite yet. They are strictly undefined irrational numbers...(although you might be able to approximate them with various defined irrational numbers, if you played around with them enough, but it's not really worth it, unfortunately.)
Gammas of fractions we would usually leave in their simplest form; that is, Γ(x), where x is the fraction you are trying to express.

dVanDaHorns wrote:

Taalit wrote:Basically what I was wondering is if there is a simple (that is, in terms of 'well-known' constants like e, pi, the euler-mascheroni constant, etc.) representation of values like Γ(1/5). The gamma function is easily solved for integers as it corresponds to a shifted factorial, but no closed forms are known for any fractional arguments of Γ(z) besides half-integers. What I am wondering is if expressions representing these values that way even exist.

Oh. Yeah, there haven't been any breakthroughs in that domain, just quite yet. They are strictly undefined irrational numbers...(although you might be able to approximate them with various defined irrational numbers, if you played around with them enough, but it's not really worth it, unfortunately.)
Gammas of fractions we would usually leave in their simplest form; that is, Γ(x), where x is the fraction you are trying to express.

Well, if I remember well, the formula for half integers, uses the "double factorial" divided by a power of two, with a factor of sqrt(pi) (a very logical way of extending factorials, if you ask me). So I guess you could define multiple factorials analog to the double factorial, and divide them by the power of the corresponding number. And as for the factor, well, probably it would be sqrt(2*pi/n) or something similar.

EDIT: actually, check this:
http://en.wikipedia.org/wiki/Particular ... _arguments


I only was wrong in the factor, it says that at least gamma(1/3) and gamma(1/4) are irrational trascendental constants on their own. It also suggests a formula for gamma(1/4). Now with millions of digits of either constant you can always try to guess some formula at home in your computer, inputting several combinations of constants

EDIT: Im talking like a nerd DX

More like a genius that won a national physics compe- oh wait.

sundayfever wrote:

EDIT: Im talking like a nerd DX

More like a genius that won a national physics compe- oh wait.

Agh! you revealed my secret! XD

Agh! you revealed my secret! XD

But it's not a secret, I mean all those newspapers and reporters and paparazzi- ok I stop now.

New Pastel Forum under attack by math formulas! :O

Look at my formula, that I invented some time ago:
Player=Einstein*Liz/Murtaugh

sundayfever wrote:

Agh! you revealed my secret! XD

But it's not a secret, I mean all those newspapers and reporters and paparazzi- ok I stop now.

Well, actually I haven't been interviewed by any reporters. I do have done a radio interview about it, and appeared briefly in some forgotten newspaper. I don't know if I appeared in TV, but I know there's a video in Youtube about the ending ceremony, with me making a fool of myself, so I FORBID ANYONE OF YOU FROM LOOKING FOR IT!!

Player=Einstein*Liz/Murtaugh

So Einstein multiplied with Liz spawning players, and Murtaugh divided those players until there was one left? XD

I know there's a video in Youtube about the ending ceremony, with me making a fool of myself, so I FORBID ANYONE OF YOU FROM LOOKING FOR IT!!

Oh come ON, gimme da link!! Okay, you don't have to give me the link. But I am sure you did not make a fool of yourself. And even if you did, you have right to do so, you won the freaking competition!

No, no links! If you saw the video, you'd know what I mean, but since you aren't gonna see it you'll never know >:) mwahahah