Gamma Definition and 714 Threads

greetings . any ideas on how to evaluate this integral \lim_{T\rightarrow \infty}\frac{1}{2T}\int_{-T}^{T}\frac{\Gamma(3+it)}{\Gamma(3+it-j)}e^{ikt}dt j, k are positive constants .

Now I am wondering what would happen to the sun if it was hit by the nearest gamma ray burst (I believe the nearest one is 6.7 Light years away). Now I understand that a gamma ray burst is going to be more radiation than what the sun produces in its lifetime. I also know that the sun is just one...

Homework Statement So my question is related somehow to the Fierz Identities. I'm taking a course on QFT. My teacher explained in class that instead of using the traces method one could use another, more intuitive, method. He said that we could use the fact that if we garante that we have the...

I'm having trouble doing a classic proof (integration par part and induction on r) for this : Pr(X>t)=Pr(Y ≤r−1), where X follows a gamma Γ(α = r, β = 1/λ) and Y a Poisson P (λt). Start with r = 1 (exponential distribution). I don't really understand what induction on r really means...

Why only gamma radiation...? All the radioactive elements emit either alpha, beta, never both and maybe sometimes gamma with these. But why do they emit gamma rays only? Why not X-Rays?

Homework Statement Evaluate the intergrals: a) integral of 3^(-4*z^2) dz from 0 to infinity b) integral of dx/(sqrt(-ln(x))) from 0 to 1 c) integral of x^m * e^(-a*x^n) dx from 0 to infinity Homework Equations gamma(n) = integral of e^(-w) * w^(n-1) dw from 0 to infinity The...

So we know gamma decays are directionally symmetric, but assume we have two detectors and we want to know the likelihood of two γs hitting each detector at the same time as a function of the angle between the line connecting the first detector and the source and the line connecting the second...

Homework Statement The Gamma function is given by \Gamma(x) = 0∫∞ tx-1e-t dt Evaluate 0∫∞ exp(-αy2)dy in terms of Gamma functions. Homework Equations n/a The Attempt at a Solution Honestly, I don't know where to start. I have knowledge of parametric differentiation (we use...

Given f(x; β) = [ 1/( β^2) ] * x * e^(-x/ β) for 0 < x < infinity EX = 2β and VarX = 2(β^2) Questions: Find the Maximum likelihood estimator of β (I call it β''), then find Bias and variance of this β'' 1/ First, I believe this is a gamma distribution with alpha = 2. Is that right? 2/...

Homework Statement The gamma function, which plays an important role in advanced applications, is defined for n\geq1 by \Gamma(n)=\int_0^{\infty} t^{n-1}e^{-t}dt (a) Show that the integral converges on n\geq1 (b) Show that \Gamma(n+1)=n\Gamma(n) (c) Show that \Gamma(n+1)=n! if n\geq1 is an...

$\displaystyle \sum_{n={\bf 0}}^{\infty} \frac{\Gamma(a+n)\Gamma(b+n)}{n! \Gamma(c+n)} \ \ c-a-b > 0$

Hi all, I was having trouble with this problem and hoping that someone could help me with it. A pion has a rest energy of 135 MeV. It decays into two gamma rays, bursts of electro magnetic radiation that travel at the speed of light. A pion moving through the laboratory at v = 0.97c decays...

This question has gone unanswered by our friends in nuclear/atomic threads. My question relates to a solitary Tc^99m decay in particular, and to gamma rays in general. If light is a collapse able wave function, are different wavelength energies the same, ie gamma, x, radio, etc. My...

I have a gamma function in the form of Gamma(s-1) where s can take only positive values. How can I plot this function for different value of s using Mathematica ?

Homework Statement Fy(y) = 1/2 λ^3 y^2 e^(-λy) Assume E(1/y) = λ/2 Find E(1/y^2) and prove Var(1/y) = λ^2 / 4 Homework Equations E(y) = k/λ Var (y) = k/ λ^2 The Attempt at a Solution Hi guys, From the equation given from gamma distribution, I understands clearly that to get...

Finding the mean of the gamma distribution ("reparameterise") Homework Statement Find the mean of the gamma distribution. f_{X}(x) = \frac{e^{-kx}x^{r-1}k^{r}}{(r-1)!} x>0, r ε N*, k>0 Homework Equations Interestingly this is the alternative form of the gamma distribution The...

I would like to have a general formula, and I am quite sure it must exist, for: \gamma^{\mu}_{ab}\gamma_{\mu \,\alpha\beta} but I didn't succeed at deriving it, or intuiting it, I am troubled by the fact that it must mix dotted and undotted indices.

Homework Statement Solve the integral annd express it through the gamma f Homework Equations cos(theta)^(2k+1) The Attempt at a Solution

I read earlier that the photoelectric effect is when electromagnetic radiation essentially overcomes an electrons binding energy and converts it to electricity, which is how solar panels function. But why is it that gamma radiation isn't being used to capture energy? If gamma radiation has a...

Hi! I can define \gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3 I know that the four gamma matrices \gamma^i\:\:,\;i=0...3 are invariant under a Lorentz transformation. So I can say that also \gamma ^5 is invariant, because it is a product of invariant matrices. But this equality holds: \gamma...

Homework Statement \int_0^∞ x^2exp(-x/2) dx Homework Equations The Attempt at a Solution Using u substitution: u = x/2 du = 1/2 dx \int_0^∞ 4u^2exp(-u) du*2 = 8 \Gamma(3) = 8*3! = 48 But the correct answer is 16 when I plug it in Wolfram's definite integral...

Homework Statement I'm trying to find P_L \displaystyle{\not}p P_L for a left-handed particle. (I think the answer is zero...) Homework Equations P_L = \frac{1}{2} (1-\gamma_5) (the left-handed projection operator) \displaystyle{\not} p = \gamma_\mu p^\mu (pμ is the 4-momentum) (γμ, γ5 are...

Homework Statement Prove by induction that gamma(v+1)(v+1)(v+2)...(v+k)=gamma(v+k+1) for k=1,2,3... Homework Equations Really just using the relation x*gamma(x)=gamma(x+1) The Attempt at a Solution for a basis gamma(v+1)(v+1)=gamma(v+1+1) so holds for k = 1 inductive...

Do I take the derivative of the density fct and set it equal to 0, then solve for t?

let X~gamma(x,λ), Y~gamma(y,λ) then Z = X+Y is gamma (x+y, λ) I'm trying to prove this. Is using the moment generating functions the only way to do it. and in such case, can I assume that MZ(t)= MX(t)*MY(t)

For my advanced physics lab course this semester, I recently conducted an experiment using a hyper-pure germanium detector to measure the energy of gamma rays released upon the formation of deuterium (DF). Essentially, I used a neutron source to bombard a hydrogen rich target (used both...

Homework Statement Find the expected value of g(X) = Xk for the a. gamma distribution b. beta distribution c. lognormal distribution Homework Equations gamma distribution: \frac{x^{\alpha -1}e^{ \frac{-x}{\beta}}}{ \Gamma (\alpha ) \beta ^{\alpha }} with paramenter x>0 beta...

Hi all, I am currently reading and calculating stuff on Next-To-Leading-Order calculations and I came across a paper that I want to calculate by myself and try to get the same results. There is one part, though, where I have absolutely no idea how this works. It comes in the context of...

http://science.nasa.gov/science-news/science-at-nasa/2011/18oct_600mysteries/ "Fermi sees gamma rays coming from directions in the sky where there are no obvious objects likely to produce gamma rays," says David Thompson, Fermi Deputy Project Scientist from Goddard Space Flight Center...

\Gamma(x)=\int^{\infty}_0t^{x-1}e^{-t}dt \Gamma(\frac{1}{2})=\int^{\infty}_0\frac{e^{-t}}{\sqrt{t}}dt= take t=x^2 dt=2xdx x=\sqrt{t} =\int^{\infty}_0\frac{e^{-x^2}}{x}2xdx Why here we can here reducing integrand by x?

Homework Statement (7.) If its kinetic energy is 3000 MeV, find its speed as a multiple of c. In this case you cannot use the nonrelativistic approximation. m=4000 MeV/c^2 (rest energy=4000MeV) ^from previous problem, of which this one is a continuation Homework Equations...

I am by no means well versed in nuclear power, but from my limited exposure I have gathered that a very large portion of nuclear energy (and antimatter) is expressed in high energy gamma radiation. All forms of electromagnetic radiation are expressed as photons, correct? Taking the concept of...

If the Gamma function \Gamma (z) = \int_0^{\infty} t^{z-1} e^{-t}\;dt only converges for \text{Re}(z)>0 then why is, for example, \Gamma (-1+i) defined when clearly \text{Re} (-1+i)<0 ?

Homework Statement In my honours lab we had to perform the Gamma ray experiment in which we have to measure the operating voltage of a Geiger Muller tube for a radio active source say Cs-137. With this we want to measure the linear absorption coefficients of lead and aluminium. Test the...

http://www.bbc.co.uk/news/science-environment-15203788 Astronomers have spotted gamma ray emissions coming from the Crab Pulsar at far higher energies than expected. This challenges notions of how these powerful electromagnetic rays - like light, but far more energetic - are formed, researchers...

In the commonly used light clock concept, where a photon bounces back and forth between 2 mirrors, it is easy to see how gamma works. Gamma is simply the factor of increase in the distance that the photon has to travel between mirrors. We can fully comprehend why time slows down at the rate that...

Homework Statement Let X have a gamma distribution with parameters α and β. Show that P(X ≥ 2αβ) ≤ (2/e)2 Homework Equations f(x) = pfd of a Gamma The Attempt at a Solution I began by solving for P(X ≥ 2αβ) by doing ∫ f(x) dx from 2αβ to ∞ I set y=x/β for substitution. and I...

In a certain country, the distribution of incomes in thousands of dollars is described by a gamma distribution with \alpha = 2 and \beta = 8. What is the probability that a man chosen at random will have the following incomes? a. More than $14,000 b. At least $12,000 So I know that...

eta --> gamma gamma Could someone help me on this. Iso spin is not conserved in EM interaction. How can we say isospin is not conserved in the 'eta -> 2 gamma' decay.The eta has I =1 and I3 =0 and for the gamma I = 0 ,1. Thanks a lot

I've just started a masters in physics after a 4-year break and am having some real trouble getting back into the swing of things! We have been asked to prove some properties of gamma matrices, namely: 1. \gamma^{\mu+}=\gamma^{0}\gamma^{\mu}\gamma^{0} 2. that the matrices have eigenvalues...

What would happen to a star if it took a direct hit from a gamma ray burst? For example if a gamma ray burst from a supermassive black hole at the center of a galaxy hit a star, would the star survive? If so, how would the grb effect the star? If not, would the star explode...

Does this ever happen? p + \gamma \rightarrow n + e+ + \nu_e It seems possible, if the \gamma has enough energy, but I wonder if anyone can confirm that it happens.

Hello. Let's say that I am in a frame in which I see a rocket traveling at v. This rocket then fires a projectile forward with velocity u in its rest frame. I can find u' easily enough using the Einstein velocity addition formula. However, I recall seeing a version of the formula that uses...

What is the distribution of the difference of two gamma distributions with same scale parameter, and shape parameter of the first one is k(1+e), e -> 0 and second one is k. What i exactly want to know is the following. X~Gamma(K(1+e),\theta) Y~Gamma(K,\theta) Prob (X>Y) or P(X-Y)>0...

Gamma decays are e.m.waves ..then how describe gamma decay in terms of energy levels?

I was wondering if there is a representation of gamma matrices unitarily equivalent to the standard representation for which Dirac Spinors with positiv energy and generic momentum have only the first two component different prom zero. Anyone can help me?

Hi, The typical representation of the Dirac gamma matrices are designed for the +--- metric. For example /gamma^0 = [1 & 0 \\ 0 & -1] , /gamma^i = [0 & /sigma^i \\ - /sigma^i & 0] this corresponds to the metric +--- Does anyone know a representation of the gamma matrices for -+++...

Solve this?? There are w cakes and n people. The cakes are distributed to people randomly. Find the expected number of cakes a 'i' person can receive. The distribution is: a) Bernoulli distribution b) Binomial distribution c) Poisson distribution d) Uniform distribution e)...

If a random variable X follows Gamma Distribution Function with parameters K and thita, what does (X+k) follow? if K is a constant. I think, since adding the constant is just like shifting the origin, the nature of the curve remain unchanged. But what about its parameter? Thanks.

Hi everybody, We know that light is an electromagnetic wave.gamma rays are e.m.waves. Both of them have the same speed 3*10^8 m/s. Gamma ray have the property to penetrate in materials like wood,cement wall etc. But,light is not penetrating even in a single wood. What is the reason behind...