posted
I have another question concerning math and if anyone feels up to it, you are most welcome. Disappointingly, it's not very involved and won't take hours to produce a post on it, so I offer my apologies before hand...
Can anyone describe to me how to go about solving an equation with "gamma" in it? I'm taking Algebra II and I don't take calculus, but I need knowledge of some of it for a project. Take this for example:
99-(square root of 9 ) - gamma - (square root of 9 )
How would you go about solving this? Does gamma have a fixed value? I would suppose not, but...what is its value when expressed with variables and/or numbers?
If anyone knows, I would greatly appreciate your help. Posts: 667 | Registered: Aug 2003
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posted
I don't understand: you have no equals in your equation. (Or < or > and so on.) Your equation is like saying "Flour mixed with eggs." and thinking that you have a sentence because "mix" is a verb.
Similarly, if you just give me numbers, arithmetic operations (+, -, *, /) and a variable, I don't know what it means to solve this.
Posts: 643 | Registered: Feb 2000
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posted
Dude, you're in algebra II and you're doing stuff with gamma? I went through Calculus AB and I have no idea what the hell that is. I also couldn't understand your last math problem. Does that reflect poorly on me or my teachers?
Posts: 1658 | Registered: Sep 2003
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quote: I'm pretty sure he means that he wants to evaluate expressions with gamma in them, not necessarily solve equations.
That's more precise - sorry, I should've said "expression", not "equation".
Perhaps I should say that I need to know how gamma functions in any situation, so that I can then evaluate an expression that contains gamma. Sorry if I wasn't clear - Posts: 667 | Registered: Aug 2003
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posted
Rabbit already defined gamma in your previous thread. "gamma(x) = integral from 0 to inf of t^(x-1) exp(-t) dt.
The gamma function interpolates the factorial function. For integer n, gamma(n+1) = n! (n factorial) = prod(1:n)."
or gamma(m)=(m-1)!=(m-1)*(m-2)*(m-3)*...*3*2*1 for integer m.
It's fairly obscure, you won't use it until calculus and even then only once or twice if ever in high school level calc.
Posts: 6316 | Registered: Jun 2003
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posted
Gamma has a few standard meanings in pure math. There's the module group that's impossible to explain unless you know some modern algebra; there's the function that (among many other things) generalizes the factorial operator to complex numbers; there's the Euler-Mascheroni constant that can be used to compute the gamma function as an infinite product; and there's the distribution in statistics that's related to the common Poisson distribution but can be computed from the gamma function. There are tons of physics connotations -- here are a few. I give these as teasers for the math-heads in the audience, as I highly doubt any of it has to do with your high school homework.
Assuming you've stated the problem correctly, I would evaluate the expression* as "93 - γ".
*remember the difference between this and solving an equation from pre-algebra?
Posts: 1839 | Registered: May 1999
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quote: It's fairly obscure, you won't use it until calculus and even then only once or twice if ever in high school level calc.
Morbo, something sporadic can be good...
quote: *remember the difference between this and solving an equation from pre-algebra?
Two years ago I took advanced algebra, and geometry and trig last year, so I wouldn't remember that - j/k. Yes, I remember that from the last few years of math, but it slipped my mind at the moment Posts: 667 | Registered: Aug 2003
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posted
Is it a capital Gamma or a small Gamma. I know some funky contstants that use a little gamma from physical chemistry, but I think you probably want the capital Gamma which I never used until my second semester of differential equations which would be in my sixth semester of college level math. I vaguely remember that it has something to do with the heaviside function.
posted
OK you can find the Gamma function explicitly defined in the table of integrals in the CRC handbook of chemistry and physics. I would reccommend looking it up yourself because it is hard to type it correctly. In my old edition it was integral #597. They also have a more complete definition if you look in the index under "gamma function"
It is the solution of the integral from zero to infinity of x^(n-1)* e^(-x) dx
One of the more useful properties: Gamma(n)= (Gamma(n+1))/n
Also Gamma (1/2)=sqrt(pi)
Posts: 11265 | Registered: Mar 2002
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posted
Well, if it is a capital Gamma and then the square root of 9 is right after it in parenthesis, meaning "Gamma of square root of 9" then that makes sense.
For any positive integer k, Gamma(k)=(k-1)! so in this case Gamma(SquareRoot(9))=Gamma(3)=(3-1)! and you can finish the computation from there.
I tend to doubt this would show up in an Algebra class without calculus though. In general, the gamma function is like the factorial (shifted by one) in that Gamma(x+1)=xGamma(x), but that formula is useless without some sort of starting value (analogous to 1!=1) to compute from. As the rabbit posted, you can define Gamma by:
Gamma(x)=integral_0^infinity e^{-t} t^x dt/t
and then it is a nice excercise to prove by integration by parts that this gives Gamma(x+1)=x Gamma(x).
I know a few other definitions, but they all need calculus. Has your teacher een talking about factorials or gamma at all?
Posts: 643 | Registered: Feb 2000
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posted
Thanks, luthe, that link led me to a generalization of the factorial function which I had never heard of, the double factorial n!!Posts: 6316 | Registered: Jun 2003
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posted
what are you doing in algebra 2 that you need the generallize the factorial for?
The first time i did stuff like that was with the statitically thermo in pchem 2. which was like spring of my sophmore year of college.
Posts: 1621 | Registered: Oct 2001
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posted
Wieczorek is in high school. My high school days are a distant memory. He was looking for weird real functions to do a homework problem, someone suggested Gamma.
I don't ever remember using Gamma in years of pursuing a BS in math, except once or twice in a problem set.
posted
Morbo's correct, Hollow Earth. There's a thread called, "Has anyone heard of this? ENTER AT YOUR OWN PERSONAL RISK". Alot of people contributed to it - I had a project and my teacher suggested using factorial. I think it was Rabbit who first suggested using gamma.
Posts: 667 | Registered: Aug 2003
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posted
Thanks, Luthe. That link will help me justify my use of gamma that I so willingly assumed without having knowledge of its function. Posts: 667 | Registered: Aug 2003
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