[Fluffy]

I have the series 1/1 * 2/3 * 3/5 * 4/7 * 5/9....

The first part is obviously N!, but I can't find how to note the lower part in an elegant way, is there any?

[rogerclee]

zero

[P_Marlowe]

Depends, what you understand under elegant.

There exists a symbol for a product, the big greek letter for Pi,

<PI> (n/(2n-1)) from N=1 to N=??? or

<PI> ((n+1)/(2n+1)) from N=0 to N=???

the latter may be better, because it starts with zero, but maybe you
belong to the camp, which claims, that 0 is not a natural number .-).

The PI symbol is the aequivalent to the sigma symbol for sums.

The above formula is at least compact.

Additional, there may be a formular using combinatoric symbols,
I am away from math since more than 10 years agao, so I am
too rusty, but it sould be possible to find a compact formula, if
you dont want to use the product symbol.

With kind regards
Marlowe

[david_c]

Fluffy, on Feb 2 2009, 10:43 AM, said:

I have the series 1/1 * 2/3 * 3/5 * 4/7 * 5/9....

The first part is obviously N!, but I can't find how to note the lower part in an elegant way, is there any?

If you're just looking for a way to write

1 x 3 x 5 x ... x (2n-1),

then you can do this by

(2n)! / (2^n)n!.

But if you're actually trying to write the series, then do what PMarlowe said.

[Fluffy]

2n! / (2^n)n! that's what I was looking for, I could feel there was something like that. Thx David.

[JLOL]

rogerclee, on Feb 2 2009, 04:45 AM, said:

zero

LOL

[gwnn]

erm!

I am pretty sure I have learned something about

n!! being only the odd or even numbers of the factorial terms.

It might have been just a theoretical physics notation for lazy people.

edit: found it on wikipedia, n!! is either the odd or the even terms, depending if n is odd or even.

4!!=2*4
7!!=1*3*5*7

[david_c]

gwnn, on Feb 2 2009, 01:24 PM, said:

erm!

I am pretty sure I have learned something about

n!! being only the odd or even terms of the factorial terms.

Yep. That's a standard notation, though I think it's one of those things that you wouldn't use in a paper without explaining what it means. (Whereas with the simple factorial n! it's safe to assume people know what you're talking about.)

[Walddk]

david_c, on Feb 2 2009, 02:52 PM, said:

(Whereas with the simple factorial n! it's safe to assume people know what you're talking about.)

I just realised that I do not belong to "people"

Roland

[P_Marlowe]

Walddk, on Feb 2 2009, 08:36 AM, said:

david_c, on Feb 2 2009, 02:52 PM, said:

(Whereas with the simple factorial n! it's safe to assume people know what you're talking about.)

I just realised that I do not belong to "people"

Roland

Me neither.

I have never seen n!!.

But than I only listed to very few lectures
about number theory.

Maybe the term regular pops up in certain
series relevant for physics,
Bernoulli Function or something similar?

With kind regards
Marlowe

[helene_t]

JLOL, on Feb 2 2009, 11:34 AM, said:

rogerclee, on Feb 2 2009, 04:45 AM, said:

zero

LOL

"Zero" was my first thought also but of course it should be understood as a finite product.

[kenberg]

Walddk, on Feb 2 2009, 08:36 AM, said:

david_c, on Feb 2 2009, 02:52 PM, said:

(Whereas with the simple factorial n! it's safe to assume people know what you're talking about.)

I just realised that I do not belong to "people"

Roland

I feel your pain. I was once at a party where most of the guests were graduate students in the French Department, all speaking French. They could not understand why I left early, although when I said adios, amigos, that might have been a clue.

[Fluffy]

ok, there is a notation for this Thanks Csaba.

I atually prefer david's first suggestion because I have another 1/2^N that goes away with this one. (Wich I actually should have suspected given that the results of the first Ns dome manually didn't show 2^N anywhere)

This all comes because in my poker forum they started to talk about mathematic problems. There was a guy who proposed the problem, then rejected my solution wich is actually right LOL.

[gwnn]

helene_t, on Feb 2 2009, 04:31 PM, said:

JLOL, on Feb 2 2009, 11:34 AM, said:

rogerclee, on Feb 2 2009, 04:45 AM, said:

zero

LOL

"Zero" was my first thought also but of course it should be understood as a finite product.

1*3*5*7*9*... = zero when the terms grow indefinitely?

[kenberg]

Fluffy, on Feb 2 2009, 10:00 AM, said:

ok, there is a notation for this Thanks Csaba.

I atually prefer david's first suggestion because I have another 1/2^N that goes away with this one. (Wich I actually should have suspected given that the results of the first Ns dome manually didn't show 2^N anywhere)

This all comes because in my poker forum they started to talk about mathematic problems. There was a guy who proposed the problem, then rejected my solution wich is actually right LOL.

Implicit in what you are saying: The best form for an expression often depends greatly on what you are going to do next.