Gamma Definition and 685 Threads

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...

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 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?

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...

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...

Hi, After having solved some problems I encountered by using Google and often being linked to threads here, I finally decided to register, especially because I sometimes have problems for which I don't find solutions here and now want to ask them by myself :) Like the following: I am...

So apparently vacuum energy is created and destroyed within Planck time by matter, antimatter annihilation. If someone could theoretically stop or slow down time, would it be possible to tap into vacuum energy? Since annihilation creates gamma rays, I suppose vacuum energy would face the same...

Homework Statement Given that \gamma^{\mu}\gamma^{\nu}+\gamma^{\nu}\gamma^{\mu}=2g^{\mu\nu}*1 where 1 is the identity matrix and the \gamma are the gamma matrices from the Dirac equation, prove that: \gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu}=2g_{\mu\nu}*1 Homework Equations...

In a discussion recently I came across the idea of an antimatter photon rocket, to quote http://en.wikipedia.org/wiki/Nuclear_photonic_rocket#Power_sources" Looking through various sites via google I've had a few answers as to how gamma rays may be reflected, the general consensus is that it...

Homework Statement Gamma rays of energy 1.02MeV are scattered from electrons which are initially at rest. Find the angle for symmetric scattering at this energy. What is the energy of the scattered photon from this case? Homework Equations \Delta \lambda = 0.0243A (1 - cos \theta )...

I have a set of data points {xi,yi} where each yi is a Gamma distributed variable where both the shape k and scale \theta depend on i. I then fit the data points with a power law model y=a(x)b. I would like to know the probability distributions for the fit parameters a and b. Is...

I'm wondering because the gamma ray photon is smaller yet it has a higher frequency. Is it because the amount of energy that passes a single point in a second for a gamma ray is higher than that of radio waves, since a lot more photons are passing that single point that in other em radiation?

http://en.wikipedia.org/wiki/Near-Earth_supernova So we know that many people are putting hard constraints on the galactic habitability zone based on the presence of nearby supernova/gamma ray bursts. But if they *only* affect the ozone layer, then I doubt that it's as hard of a constraint as...

I am very uneducated in physics, however I did take a remote sensing course in college where we discussed EMR. My questions are the following: could gamma radiation be absorbed in a material and then transferred to another material or dispersed. I know that gamma radiation has no charge and is...

How do I calculate the integral \int_{ix}^{i\infty} e^{-t} t^{-s-1}dt, where x>0, s>0? Mathematica gives \Gamma(-s,ix), where \Gamma(\cdot,\cdot) is the incomplete gamma function, but I am not sure how to justify this formally.

is there a way to explicitly express the chi-squared inverse function? when programming it, I have had to resort to a guessing system where I find a chi value that is too low and too high, and evaluate the chi-squared CDF to reset the high and low points iteratively until it is within a...

In some exercises I've stumbled upon a function which is denoted \gamma_{m}(n) with m,n natural. I've no idea what is the definition of the function and could not infer from the exercises. Searching google yielded nothing, as it kept suggesting me the OTHER Gamma function. Can anyone here help...