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#26 Re: Help Me ! » Bound Product of Sine » 2010-03-06 13:24:32
How do I evaluate a product in the form of
?#27 Re: Help Me ! » Bound Product of Sine » 2010-03-06 12:35:17
Sorry, there was a typo in my last message. The identity is corrected now. 
#28 Re: Help Me ! » Bound Product of Sine » 2010-03-06 10:22:46
Again, I'm not sure how helpful this is but I am trying to post my progress in the problem so that if anyone has any corrections or something to add they can.
Substituting
for I get.Where
is the q-Pochhammer.Although this appears to be a closed form, the q-Pochhammer is defined in terms of
(see http://mathworld.wolfram.com/q-PochhammerSymbol.html).The q-Pochhammer can be expressed differently depending upon the range of
in . Since the product above starts at 2 and moves through n respectivally. It stands to reason that the product would be undefined if . That being said, much of the definiton can be canceled.So for the purposes above let q-Pochhammer be defined as
.Ok! Wooh. I feel like I just gave birth to an accountant. Please check over everything I did. I probably made a mistake somewhere. If you have any suggestions or ideas of your own please let me know. Thanks for putting up with my rediculious problem. 
It seems like the more I try to simplify this the more complex it gets. 
#29 Re: Help Me ! » Bound Product of Sine » 2010-03-06 09:09:39
I don't know if I am helping my cause but there using the laws of Sine. I can show:
It is clear the denominator of the fraction is increasing by powers of 2 and the outside signs of the trig functions are powers of -1. The inside of the trig functions apear to also be some kind of modulation so that every possible "combination" of addition is expressed. The trig function used is alternating between sine and cosine. Knowing this I am not sure how to express this in terms of a single
. Is it possible to do so?#30 Re: Help Me ! » Bound Product of Sine » 2010-03-05 14:23:22
No, unfortunaly this is a small part of a much larger product where both n and a are dependant varbles. 
Is it possible to express this series in terms of
only?#31 Help Me ! » Bound Product of Sine » 2010-03-05 12:25:45
- aleclarsen12
- Replies: 19
How do I go about expressing the following product without any
's or 's? Can it even be done?
#32 Help Me ! » Latitude and Longitude » 2009-03-12 13:07:50
- aleclarsen12
- Replies: 1
I am writing a program that takes peoples IP addresses and converts it to their geographical location.
I was able to write an engine that converts the IP to Latitude and Longitude.
Now I want to display this on a small image map (show below).
The problem is that I do not know how to convert the Latitude and Longitude to X,Y cords on the map.
Just to further complicate things, in computers X,Y is different.
Although you would expect (0,0) to be in the center of the image, it is accualy in the upper right hand corner of the image.
Each interager represents 1 pixel. And everthing in the third section is positive.
I hope I explained that well. If not here is a formula(s):
New X = (-1 * OldX) - (ImageWidth / 2)
New Y = (-1 * OldY) - (ImageHeight / 2)
Thanks!:D
#33 This is Cool » irrational fractions » 2009-01-01 15:37:37
- aleclarsen12
- Replies: 2
A couple of weeks ago, my math teacher was explaining that ONLY square root and logs could have irrational values and all irrational values could be expressed with one of the 2. He also stated that no fractions are irrational in their native forum.
So I started thinking.... in therory.... pi is equel to circumpherance divided by diameter... isn't that a fraction... and isn't pi irrational.
BINGO!
Now, correct me if I wrong, but is my TEXT BOOK and MATH TEACHER wrong?
#34 Re: Help Me ! » Nested absolute value in algebraic expression » 2008-06-01 15:25:53
the technical definition of "absolute value" is:
|x|=√x²
Because a negative squared is a positive sqrt. is then positive (on its first solution of coarse)
So it is realy:
Unfortunately my 7th grade mind know not how to simplify
#35 This is Cool » ∞+½=½ » 2008-06-01 15:13:24
- aleclarsen12
- Replies: 9
This makes no sence...
∞+1/2=1/2
Did I do something wrong.. or is this right?
#36 This is Cool » Every math lover's dream... » 2008-06-01 10:34:25
- aleclarsen12
- Replies: 4
I was sitting and thinking (I seen to do that alot. lol) and I had this intresting revalation:
Being in the 7th grade we concide the square root of a negative "undefiend".
Well, I dawned on me that you could just do this: sqrt(-16)=-16^1/2*sqrt(-1)
My math teacher informed me this already existed and they were called imaginary numbers. (I was crushed)
A few days later I was thinking (see what I mean) and I had another revalation. The square root of a imaganary number could be expressed as the 4th root of -1. So I wrote this formula:
A stands for alternate number line. Where N is the number line. Ex N=0 (Real Numbers) N=1 (Imaginary) N=2 (Imaginary root?) ect.
Has this already been invented? (Just crush me now)
IF NOT I HAVE FUFILED MY DREAM!!!! TO ONE WRITE MY OWN USEFUL FORMULA!! (No matter how obvious it is)