Gamma function Definition and 125 Threads

Homework Statement \int e^{-\frac{2Zr}{a}}*r^{-1}dr Boundaries:[0,R] Homework Equations --- The Attempt at a Solution I tried to solve this with lower incomplete gamma function and got \gamma(0,\frac{2ZR}{a}) which is infinite i think. Z=81,a:Bohr radius,R=r0*A^(1/3)...

I Heard That the gamma function explains the strong nuclear force . \Gamma \left( z \right) = \int\limits_0^\infty {t^{z - 1} } e^{ - t} dt How does it explain the Force? Thanks

what is the simplification of the following expression (in terms of gamma and\or other functions) ? \Gamma(xy) i tried the following : \Gamma(xy)=\int^{\infty}_{0} t^{xy-1} e^{-t} dt now let t^x = s => ( after some manipulation ) \Gamma(xy)=\frac{1}{x}\int^{\infty}_{0} s^{y-1}...

maple syntax: int(theta^y * exp(-theta*(1-alpha) ) , theta) I have a distribution that I need to integrate, and I know the result should have a gamma function in it. The only thing I have found helpful is: http://en.wikipedia.org/wiki/Gamma_function My function is kind of in that...

Will some one help me to prove this identity G(n)+G(1-n)= pi/ sin npi 0<n<1 B(m,n) = (m-1)! / n(n+1)...(n+m+1) ,for beta function

The http://en.wikipedia.org/wiki/Gamma_function" is the integral \Gamma(z)=\int_{0}^{\infty}{dt\, t^{z-1}e^{-t}} . It has poles for integers of z less than 1 and is finite everywhere else. But to me it seems like it should be infinite for non integer values of z less than 0. My reasoning...

Homework Statement Need to prove these 2 identities of beta function & gamma function ? Homework Equations G(n)G(1-n)= pi/sin npi B(m,n) = (m-1)! / n (n+1)...(n+m+1) The Attempt at a Solution I tired using beta function in 1st one but did not get the solution .

[SOLVED] Regression Analysis for a Gamma function My regression analysis program that I developed in BASICS back in the 1980's applies for half a dozen linear equations some of which are transormed into log forms. I would like to modify my program to include this Gamma function...

Hello, I need to compare an exponential integral -E_{-2k}(-m) -where k is a positive integer and m just a real number- to a Gamma function \frac{1}{m^{2k+1}}\Gamma(2k+1). I am using the notation from Mathworld here http://mathworld.wolfram.com/ExponentialIntegral.html...

Hi The compound summation formula v = \frac{(m + l)!(al + a + cm)}{m!(l + 1)!} listed in the "Solve v = f(x) for x" thread uses factorials and in an effort to extend it to non-integral values of "m" and "l", I stumbled across the gamma function http://en.wikipedia.org/wiki/Gamma_function" ...

Has anyone seen this representation for gamma function before? \Gamma(z) = \int_0^1\ dt\,\, t^{z-1}(e^{-t}\, -\, \sum_{n=0}^N\frac{(-t)^{n}}{n!})\,\, +\,\, \sum_{n=0}^N\frac{(-1)^{n}}{n!}\frac{1}{z+n}\,\, +\,\, \int_1^\infty dt\,\, e^{-t}\,t^{z-1} for Re(z) > -N-1 I can't figure out how...

Hey , i am in grade 11 not yet studied gamma function, and not sure if it will be in the program but i have studied it a bit on my own f(x) = gamma(x) x = 1 : y = 1 x = 2 : y = 1 x = 3 : y = 2 x = 4 : y = 6 x = 5 : y = 24 x = 6 : y = 120 and i found a pattern : 1 * 1 = 1 2 * 1 = 2 3 * 2 = 6...

Hi gang, I'm having trouble with doing a derivative of the Gamma function. I know both the definition of Gamma and Polygamma, but can't see how to get from the derivative of Gamma to Psi times Gamma. Any help or hints would be great. Thanks!

Question: A particle of mass m starting from rest at x=1 moves along the x-axis toward the origin. Its potential energy is V=\frac{1}{2}mlnx. Write the Lagrange equation and integrate it to find the time required for the particle to reach the origin. Lagrange Equation in 1-D...

For what values of k would \mathop {\lim }\limits_{x \to \infty } \frac{{\Gamma \left( {kx + 1} \right)}} {{x^{kx} }} converge?

Hiya, I'm having trouble finding a simple proof for gamma of 1/2 = root pi? Any suggestions

The given problem is this: Solve using the gamma function \int_0^{\infty}\sqrt{x}\exp{^{-x}}{ dx}My problem is that I don't know how to use the gamma function. It doesn't make sense to me...any insight would be helpful. Thanks in advance

I am wondering how the following statement holds true: \Gamma\left(\frac{1}{2}\right)=\int_0^{\infty}e^{-x}x^{-\frac{1}{2}}\,dx=\sqrt{\pi} I know how to show that: \int_0^{\infty}e^{-x^2}\,dx=\frac{\sqrt{\pi}}{2} But I can't seem to apply that method (converting to a double-integral) to the...

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...

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...

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...

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?

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...

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...

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...