How to Prove Gamma and Beta Function Identities?

AI Thread Summary
To prove the identities involving the beta and gamma functions, the first identity states that G(n)G(1-n) equals pi/sin(n*pi). The second identity defines the beta function as B(m,n) = (m-1)! / (n(n+1)...(n+m+1)). The original poster attempted to use the beta function for the first identity but was unsuccessful. They suggested that the discussion might be better suited for a math homework help forum. Further insights or methods for proving these identities are needed.
mkbh_10
Messages
217
Reaction score
0

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 .
 
Physics news on Phys.org
Maybe move this post to one of the math HH forums?
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »
Thread 'Voltmeter readings for this circuit with switches'

Thread 'Voltmeter readings for this circuit with switches'

TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
View full post »
Thread 'Trying to understand the logic behind adding vectors with an angle between them'

Thread 'Trying to understand the logic behind adding vectors with an angle between them'

My initial calculation was to subtract V1 from V2 to show that from the perspective of the second aircraft the first one is -300km/h. So i checked with ChatGPT and it said I cant just subtract them because I have an angle between them. So I dont understand the reasoning of it. Like why should a velocity be dependent on an angle? I was thinking about how it would look like if the planes where parallel to each other, and then how it look like if one is turning away and I dont see it. Since...
View full post »

Similar threads

Can Geiger Counter Ticks be converted into particle/wave counts?
Replies
12
Views
2K
How to calculate gamma ray energies following beta decay?
Replies
12
Views
1K
Is Exponential Form Better for Balloon with Inserted Load Calculation?
4
Replies
170
Views
7K
Special relativity and acceleration
Replies
3
Views
1K
What is the meaning of the intercept of a particular solution to damped oscillator?
Replies
7
Views
936
Estimating damped harmonic oscillator parameters from this plot of the oscillations
Replies
9
Views
2K
Interference pattern of a fan of plane waves
Replies
2
Views
2K
Find the Coefficient of Kinetic Friction
Replies
5
Views
2K
Maximizing Range/Time in Air of an Airplane: Solving with Calculus
Replies
4
Views
2K
Understanding the Differences Between Bose and Classical Gases
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top