Relation Between Beta and Gamma functions

Context: Undergrad
Thread starter PLAGUE
Start date Jan 2, 2024
Tags

Beta function Gamma function

Join the discussion

Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.

Real named experts · corrections over time · the nuance an AI answer skips

1 reply · 2K views

PLAGUE

Thread starter
Jan 2, 2024

TL;DR: Proof of Beta Gamma function relation

So, my teacher showed me this proof and unfortunately it is vacation now. I don't understand what just happened in the marked line. Can someone please explain?

Physics news on Phys.org

How Gravity from Entropy theory connects the second law of thermodynamics with the emergence of cosmic structure
New optical chip design controls light speed in real time, simulations suggest
A scheme to verify gates of a quantum computer without examining devices

pasmith

Science Advisor

Homework Helper

Jan 2, 2024

The line asserts that [tex] \int_0^\infty e^{-x(1+ y)}x^{m+n-1}\,dx = \frac{\Gamma(m + n)}{(1 + y)^{m + n}}.[/tex] How would you apply the given formulae to arrive at that?

Relation Between Beta and Gamma functions

Undergrad Why ##a^0=1##?

Undergrad Finding the minimum distance between two curves

High School Arc Length for Hyperbolic Sin

Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?

High School Taking a limit and getting the wrong answer...don't know why

Undergrad Correct Upper/Lower limits for continuation of solutions for ODE

Graduate About ellipticity and a proof that a system of PDEs is elliptic

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Relation Between Beta and Gamma functions

Similar threads