Gamma Definition and 685 Threads

Prove the following $$\int^1_0 \ln\left( \Gamma (x) \right) \, dx = \ln \left( \sqrt{2 \pi } \right) $$

Homework Statement "How could you show that a radioactive source was only emitting alpha and gamma radiation?"The attempt at a solution This really stumped me...obviously they have different penetration distances, and different strengths of ionisation, but I don't know how to show that only...

e+e- --> gamma f0 --> gamma pi0 pi0 cross section with VMD Homework Statement Find the cross-section of ##e^+e^- \to \gamma f_0(980) \to \gamma \pi^0 \pi^0## using the vector meson dominance model. Homework Equations Some Feynman's rules: The photon propagator is -i...

Homework Statement Show the gamma density function integrates to 1.Homework Equations Assume α > 0, λ > 0, t > 0 g(t) = \frac{λ^α}{\Gamma (α)} t^{α-1}e^{-λt} \Gamma (α)= \int_0^∞ t^{α-1} e^{-t} dt The Attempt at a Solution Show \int_0^∞ \frac{λ^α}{\Gamma (α)} t^{α-1}e^{-λt} dt = 1...

So I have a bit of a story here. First of all, I work in my university's radiation safety department, where, among other things, I calibrate Geiger Counters. I also passed Modern Physics (Physics III), so I got some education on radioactive decay. I have an old Counter from 1962, a...

If what used to be visible light when the universe was smaller and younger has been stretched due to the Doppler effect so that it is now microwaves and detectable as the Cosmic Microwave Background Radiation that can be found everywhere, why hasn't the gamma or x-rays of the same period not...

Homework Statement A proof of equality between two traces of products of gamma matrices. Tr(\gamma^\mu (1_4-\gamma^5) A (1_4-\gamma^5) \gamma^\nu) = 2Tr(\gamma^\mu A (1_4-\gamma^5) \gamma^\nu) Where no special property of A is given, so we must assume it is just a random 4x4 matrix. 1_4...

This is mostly calculus, but the question is computer based, I think. The antiderivative of the gamma function is, fairly trivially, ##\displaystyle \int_{0}^{+\infty}\frac{t^{z-1}}{e^{t}\ln{t}}-C##, where C is an arbitrary constant. Why does Wolfram Alpha have trouble calculating the...

After performing this experiment, we will get different peaks on the computer screen, where on x-axis lies thickness of the absorber and on the y-axis the nb of channels. What do these represent exactly? Why do we have a high peak and a medium sized one? What are the significances of each...

I have to understand why someone would the Gamma Distribution, what does it tell it me when i use it or why would i use it in the first place?

Homework Statement I have a quick question about the gamma function. According to my textbook it says: \int_{0}^{\infty }{{{x}^{n}}{{e}^{-ax}}dx}=\frac{\Gamma \left( n+1 \right)}{{{a}^{n+1}}} where \Gamma is the gamma function. My question is, do n has to be an integer number, or can it also...

I do not understand the full theory behind destructive interference. Hence I need helps: 1. The topic on destructive (and constructive) interference was always discussed on light and sound wave. Will this theory applicable on other radiation such as gamma? 2. During two wavelenghts met at...

Hi I want to define an Am-Be source in MCNPX 2.6 I have Neutron spectrum But I don't have Gamma spectrum of this source. Please Help!

I have read articles about the GRB measurement using X-ray from afterglow. The article tells that the gamma ray provides poor directional information.Why? How can we use X-ray for measurement?

Homework Statement Consider a nucleus which is initially at rest and in an excited state with energy Ei. It then decays to a lower energy state with energy Ef by emitting a gamma-ray photon. Show that the energy of the photon is approximately given by Eγ≈ΔE−(ΔE)^2/(2mc^2) where ΔE = Ei - Ef...

In almost all the books on field theory I've seen, the authors list out the different types of quantities you can construct from the Dirac spinors and the gamma matrices, but I'm confused by how these work. For instance, if $$\overline\psi\gamma^5\psi$$ is a pseudoscalar, how can...

I've heard it said that relativity formally permits tachyons and that we don't believe they exist merely because there is no empirical evidence of them. However, since a tachyon's speed exceeds c, its γ must be imaginary. The t-component of the particle's 4-velocity is, depending on...

I have an unidentified radiation source. I used a NaI(Tl) detector and multichannel analyzer to collect data and plotted the spectrum. I found peaks at energies of 86.3, 123.7, and 369.6 keV. From this data I am attempting to identify the source, but I am having a difficult time. I tried using...

Hi, I would like to know why is it that gamma(1/2) = squareroot(pi) The other values as well. I don't see why out of all values that the gamma function converges to operations of pi of all things. Is there some kind of relationship to the gamma function and the trigonometric function...

I have a question about energy reconstruction. I'm writing up a paper, and I'm trying to understand why this is the reason, before putting it in my paper. I know from experimental evidence that it is the case, though I would like to know if there is a reason. Let's say you have a sufficiently...

Hi I have this integral that I want to express in terms of a gamma function. Unfortunately I am unable to bring it in this form. So can you give me a hint how wolframalpha does thishttp://m.wolframalpha.com/input/?i=∫e%5E%28ix%29%2F%28ix%29%5E%281%2F5%29dx+from+-+infinity+to+infinity&x=10&y=3

Homework Statement Hi all, I missed the day of class where we went over likelihood functions, and I'm quite confused! For example, let's say I have n Xis, where each Xi ~ Gamma(a,b), where a and b are unknown. I want to find the likelihood function of a and b, but I don't think I really...

Homework Statement This is not a problem I was assigned, I am just trying to figure out how I could prove it to myself. Basically, I am just wondering WHY the gamma value for relativistic momentum takes the form that it does, namely (1-u^2/c^2)^-.5 I've tried to prove this to myself a...

How to prove the convergence or divergence of ? $$\sum^{\infty}_{n=1}\frac{\Gamma(n+\frac{1}{2})}{n\Gamma{(n+\frac{1}{4})}}$$

Different materials emit different frequencies of radiation when heated by a source of heat such as electricity. Examples include gases and solid filaments that emit infrared, visible and ultraviolet radiation, and the scheelite calcium tungstate filaments used to produce x-rays in fluoroscopes...

Homework Statement Questions are in picture. Homework Equations $$ \int _{0}^{\infty }x^{n}e^{-x}dx $$ = $$ Gamma (n+1) = n! $$ Gamma(P+1) $$ = $$Gamma(P)$$ $$ Gamma(P) = (1/P) $$Gamma(P+1)$$ The Attempt at a Solution 2) I have found it from table. 3) I have used recursion and...

Homework Statement (a) The ratio v/c is very often denoted by the single symbol β. Show that if β<<1, the following are valid through terms of order β^2 E = mc^2 + (mv^2)/2 = (mc^2)[1+(β^2)/2] K = (mv^2)/2 = (mc^2)[(β^2)/2] pc = mvc = m(c^2)β γ = 1+(β^2)/2 (b) Show that if γ = ε^-1...

I need to get all the information I can about it. Is their a good source for that info?

Hi there, I'm actually trying to understand why the behaviour of the Gamma function at z = -n is (-1)^n/(n!z) + O(1) The first term (although without the z) I recognized it as the residue of f when z= -n. But the rest, no idea. Any explanation is very appreciated.

Dear all I am working with a Gamma-Poisson mixture distribution where (and this is not usual) the support of the Gamma distribution (in fact, I am able to restrict to the neg exponential instead of the Gamma...) is finite, e.g. [0,1]. I would like to derive the mean and a Likelihood...

Homework Statement Let g(x) = \frac{1}{x+c}, where c is a positive constant, and x is a random variable distributed according to the Gamma distribution x\sim f(x)=\frac{1}{\Gamma(\alpha) \beta^\alpha} x^{\alpha \,-\, 1} e^{-\frac{x}{\beta}}. I wish to calculate the expected value of...

http://arxiv.org/abs/1206.1616 Strong Evidence for Gamma-ray Line Emission from the Inner Galaxy - Meng Su, Douglas P. Finkbeiner Analysis of data from the Fermi telescope shows "monochromatic" gamma ray emission at 130 GeV from the centre of the galaxy. This paper is generating a lot...

\Gamma(n) = int(0 to infinity)[(x^(n-1))*e^-x]dx Show that it can also be written as: \Gamma(n) = 2int(0 to infinity)[(x^(2n-1))*e^(-x^2)]dxI have no idea how to go about this. I have tried integration by parts of each to see if anything relates, but how can you get from an exp(-x) to and...

So if the parameter \theta is alpha... L(\theta) = \frac{1}{\Gamma(\theta)\beta^{\theta}} x^{\theta-1} e^{-x/\beta} Now I take the natural log of that... ln(L(\theta)) = ln(\frac{1}{(1-\theta)!}) + ln(\frac{1}{\beta^{\theta}}) + ln(x^{\theta-1}) + ln(e^{-x/\beta}) Now I want to...

Homework Statement Find the probabilities that the value of a random variable will exceed 4 if it has a gamma distribution with (a) \alpha = 2 and \beta = 3 (b) \alpha = 3 and \beta = 4 [b]3. The Attempt at a Solution [/b} how would I even attempt this question?

Hello there. I am wondering if anyone can shed some light on this topic. I am searching all over the Internet to find reliable sources on the possibility of gamma ray lasers. I know that it requires an atom that can be "pumped" without spontaneously emitting its energy so it can be triggered by...

But high frequency are absorbed, like gamma rays. I would think it would be the opposite. So what's the physical reason?

The time it takes to complete a project is a random variable Y with the exponential distribution with parameter β=2 hours. Apply the central limit theorem to obtain an approximation for the probability that the average project completion time of a sample of n=64 projects undertaken...

Let Y|X be a Poisson(X), and X be Gamma(\alpha, \beta). Find E(X|Y)... Since Y|X is Poisson(X), we have f(Y|X)= \frac{m^x e^{-m}}{x!}... Since X is Gamma(\alpha, \beta), we have f(x)= \frac{x^{\alpha-1} e^{-x/B}}{\Gamma(\alpha) \beta^{\alpha}}... Since f(Y|X) = \frac{f(x,y)}{f(x)} ====>...

Several elementary particles emits gamma radiation Where can I read more about the different magnitude?

Hello, I was just curious if anyone knew of a single place with a list of many different gamma matrix representations, I haven't been able to find what I want by just searching google. In particular, I'm looking for a representation of the 5+1 dimensional Clifford algera. In other dimensions...

what do u mean by gamma ray branching ratio of 'k-40' is 10.67%?

I was searching for derivative of factorial. Many say that gamma function is the derivative of the factorial. Is that true because I searched about gamma function and it doesn't say anything like that. Thanks a lot

Homework Statement A radioactive source which is known to emit gamma rays only at a single energy is placed in front of a gamma ray detector. The gamma ray pulse height spectrum shows three distinct pulse heights of 7.38,6.49 and 5.60 volts. What is the energy of the gamma ray? The Attempt...

Generally, Gamma matrices with one lower and one upper indices could be constructed based on the Clifford algebra. \begin{equation} \gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij}, \end{equation} My question is how to generally construct gamma matrices with two lower indices. There...

Homework Statement Just a matter of convention (question) Homework Equations \gamma^0 = \begin{pmatrix} 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & -1 & 0 \\0 & 0 & 0 & -1 \end{pmatrix} The Attempt at a Solution If then, \gamma^0 = \begin{pmatrix} 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0...

Homework Statement The absolute value of the gamma function \Gamma (x) that is defined on the negative real axis tends to zero as x \to - \infty . Right? But how do I prove it? Homework Equations The Attempt at a Solution I've tried to use Gauss's Formula...

Homework Statement Solve the equation. What is it's trace?Homework Equations k γμ γ5 o γ\nu γ5 The Attempt at a Solution I don't think this is reduced enough. γμkμγ5γ\nuo\nuγ\nuγ5 trace: just got rid of gamma5 with anticommutation. -Tr[γμkμγ\nuo\nuγ\nu]

\pi = \frac{\partial \mathcal{L}}{\partial \dot{q}} = i \hbar \gamma^0 How do I expand i\hbar \gamma^0 the matrix in this term, I am a bit lost. All the help would be appreciated!

Or light rays for that matter. Where does the window open in the atmosphere on the em spectrum, UV? Why is that?