Gamma Definition and 685 Threads

I am trying to follow a proof of \Gamma(\frac{1}{2}) = \sqrt{\pi} but in the way i have found this equality: \int_{0}^\frac{\pi}2sin^n xdx = \int_{0}^\frac{\pi}2cos^n xdx. I have tried unsucessfully integration for parts and I don't see how can I make some substitution. Maybe you can help...

Gamma Rays of wavelength 0.710 Angstrom are scattered in a thin foil of Aluminium. The scattered radiation is observed at an angle of 60 degree from the incident direction. What wavelength would u expect to see? Thanks in advance

http://arxiv.org/abs/astro-ph/0506520 Title: Dark Matter Annihilation: the origin of cosmic gamma-ray background at 1-20 MeV Authors: Kyungjin Ahn Eiichiro Komatsu Comments: 5 pages, 3 figurs; submitted to PRD, Rapid Communication The origin of the cosmic gamma-ray background at 1-20 MeV...

I've been searching the internet for a reasoanable explanation for the fenomenon and one observation of a GRB 8 billion light years from Earth tranformed 1.3 times the mass of the sun into gamma radiation and 16 days later they detected a new blue galaxy with stars already forming. Can someone...

Hi, I'm new. I read aboot how an electron, and a positron colliding is supposed to produce two separate gamma rays in completely opposite directions 180 deg away from each other. I understand that the gamma rays are supposed to correspond perfectly to the mass of the particles involved. I am...

Greetings, I've been asked to prove the following identity tr(\gamma^{\mu} \gamma^{\nu} \gamma^{\rho} \gamma^{\sigma}) = 4 (\eta ^{\mu \nu} \eta ^{\rho \sigma} - \eta ^{\mu \rho} \eta ^{\nu \sigma} + \eta ^{\mu \sigma} \eta ^{\nu \rho}) I know that tr(\gamma^{\mu} \gamma^{\nu}) = 4...

I just learned induction in another thread and I'm curious if it can be used to prove that the gamma function converges for p\geq0. I'm not sure if it can be used in this way. Is this wrong? Gamma Function is defined as: \Gamma(p+1)=\int_0^\infty e^{-x}x^p \,dx We're trying to show that this...

i heard some breaking news about a gamma ray emission which is confusing some scientists. did anyone heard about it?

Hi. I'm having some trouble solving the following gamma function: Evaluate the integral e^(4u) * e^(-e^u)du. The upper limit is inifinity and the lower limit is 0. I'm letting x = e^(u) or u = 1 in the hope to have the function looking similar to the gamma function. But I'm having no...

Hi! I hope this is the correct section to post this question in. What's the difference betwen \gamma-decay and photons? Thank you in advance.

I've been trying to determine how certain definite integrals are expressed in terms of Gamma functions. Mathematica returns the following: \int_0^1 \frac{dx}{\sqrt{1-x^4}}=\frac{\sqrt{\pi}\Gamma[\frac{5}{4}]}{\Gamma[\frac{3}{4}]} (Mapple returns a different but equivalent expression in...

In other medium except vacuum, there is different speed in different EM wave, right? i.e. speed of radio wave is faster than speed of gamma wave, right?

What is the recoil energy (in eV) of a 57Co nucleus emitting a 14.4 keV gamma ray? If anyone knows the equation that I can use, thanks.

Recall that every point (x, y) in the plane is described by its radius- vector r = xi + yj. A planar curve [gamma] has the following geometric property: at every point on the curve the radius vector and the tangent intersect at a fixed angle [alpha]. 1. Derive a first order differential...

so I don't even know where to start and how to approach this. suppose that a set of measurements y1, y2,...y100 were taken from a gamma pdf where E(y)= 1.5, and var(y) = .75. how many y(i's) would I expect to find in the interval (1.0, 2.5). I have absolutely no idea where to start given my...

Hey I was given 3 problems for homework, I just need help on some and the others I want to make sure i did it right. Problem 1: What is gamma for an object with speed B = 0.1? Problem 2: You are at rest, and see me as moving with a speed of B = 0.05. I see a car moving with a speed of B =...

I'm new to the whole relativity thing, and I've been reading the book E=mc^2, The Equation That Changed the World. I don't know if any of you have read the book, but, in the book, give the gamma factor equation, gammefactor=1/sqrt[1-(v/c)^2], now, here are my questions. 1.) What really does...

X-ray energies increase with atomic number, Z. X-rays originate from photon emissions as electrons drop back into the K and L shells of atoms. Thus they have characteristic wavelengths. Hydrogen has the lowest energy X-rays (Ek=13.6 eV) which is the first ionzation potential. It has one...

The definition of this function is Gamma(z) = integral(0, inf)(t^(z-1)e^(-t) dt) Well, I can't understand what the t stands for. The only parameter is z... Is it an arbitrary number?

A Fe (57) atom is in an excited state 14.4 keV above the ground state. The nucleus decays to the ground state with the emission of a gamm ray. What's the recoil speed of the nucleus? I'm not sure how to set this up. I thought a photon would have no mass, therefor no momentum. If so I...

Hi everyone, From the condition: \gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu} = 2g_{\mu\nu} how does one formally proceed to show that the objects \gamma_{\mu} must be 4x4 matrices? I unfortunately know very little about Clifford algebras, and for this special relativity project...

By definite integral, gamma function can be defined as \Gamma(z)= \int_{0}^{\infty} t^{z-1}e^{-t} dt I've learned some properties of Gamma function but my lecturer didn't tell us the domain of Gamma function. (I'm assuming it is defined for all non-negative real numbers). I thought of...

I was just thinking, nuclear fusion in the core of a star produces a gamma ray burst that takes about one million years to reach the surface of the star where it becomes visible light. Why does it take the gamma ray one million years to reach the surface if it is traveling at light speed? I...

Would a quark-gluon plasma reflect x rays and gamma rays and would such a plasma exist in gamma ray bursters and black holes?

Hi, can someone tell me the extinction coefficient of a gamma ray in the atmosphere? How far does a gamma beam go in the atmosphere before its intensity reduces to half or to 1/e?

What causes the short-lived, highly energetic, flash of light emitted by some black holes as they are created?

i get what alpha is but i do not really get what betta and gamma is can someone please explain to me ? thanx

can someone explain what a gamma burst is in simple terms... thanks.

This Paper may be large, but it is a must for some pretty far reaching consequences for Cosmology. http://uk.arxiv.org/PS_cache/astro-ph/pdf/0312/0312347.pdf I will astounded if the paper is not seen in the near future as a remarkable paper of astronomical foresight and will be a paper...

Does anybody know if it's possible to evaluate the gamma function analytically? I know it becomes a factorial for integers, and there's a trick involving a switch to polar coordinates for half values, but what about any other number? I have tried using a Taylor expansion and residue...

It's embarassing to have to ask this, but I have never seen this issue discussed. Is there an upper limit on the energy of the gamma rays from the gamma ray bursts? Namely 1.022 MeV? Because any gamma ray of that energy or greater can and will produce pairs of electrons and positrons by...

some news about the origin of gamma ray bursts, this may be old news to some.there have been many theories for the production of gamma rays, it seems now that the search is narrowing. http://www1.msfc.nasa.gov/NEWSROOM/news/releases/2003/03-041.html Using NASA's Chandra X-ray...

http://www.newscientist.com/news/news.jsp?id=ns99994198

Hello, can anyone please me here? I need to prove that int(x^a(lnx)^b.dx= (-1)^b/((1+a)^b+1)*Gamma(b+1) by making the substitution x=e^-y this is what I have done so far: x=e^-y -> y=-lnx x=0 -> y=-(-00) =+00 x=1 -> y=0 dy/dx = -1/x -> dx=-xdy =-e^-ydy then the integral...

This may be a dumb question: What is it about radioactivity that caused them to name it "radioactive"? All I was taught was that radioactivity is an emission of gamma particles, beta particles, or alpha particles. I don't remember anything about radio wavelength photons.