A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Find the solution of gamma and beta function!
anonymous
 3 years ago
Find the solution of gamma and beta function!

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Find the solution of gamma and beta function for \[\int\limits_{0}^{\pi/2} \frac{ d \theta }{ \sqrt{\sin \theta} }\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@ajprincess @amistre64 @BAdhi

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0i dont have enough experience with beta and gamma

ajprincess
 3 years ago
Best ResponseYou've already chosen the best response.0I am sorry @gerryliyana I havnt learnt this.:(

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I don't understand your original question, but this is an elliptic integral.

abb0t
 3 years ago
Best ResponseYou've already chosen the best response.1If the root wasn't there I would have an idea but it's making it a problem with it there.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@gerryliyana can you state more clearly what you wish to do?

abb0t
 3 years ago
Best ResponseYou've already chosen the best response.1Isn't it \[\frac{ \Gamma (m) }{ 2 \times \Gamma (m) }\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ok ok...,for eample i have \[\int\limits_{0}^{\pi/2} \frac{ d \theta }{ \sqrt{\sin \theta} } \] based on Beta function; \[B(p,q) = 2 \int\limits_{0}^{\pi/2} (\sin \theta)^{2p1} (\cos \theta)^{2q1} d \theta \] then, i have \[\int\limits_{0}^{\pi/2} \frac{ d \theta }{ \sqrt{\sin \theta} } \] \[\int\limits_{0}^{\pi/2} (\sin \theta)^{1/2} (\cos \theta)^{0} d \theta\] \[\int\limits\limits_{0}^{\pi/2} (\sin \theta)^{2 (1/4)1} (\cos \theta)^{2 (1/2)1} d \theta \] then i have \[B(p,q)=2 \int\limits\limits\limits_{0}^{\pi/2} (\sin \theta)^{2 (1/4)1} (\cos \theta)^{2 (1/2)1} d \theta \] \[\int\limits\limits\limits_{0}^{\pi/2} (\sin \theta)^{2 (1/4)1} (\cos \theta)^{2 (1/2)1} d \theta = \frac{ 1 }{ 2 } B(p,q)\] with p = 1/4 and q = 1/2; then (relation Beta and gamma) \[B(p,q) = \frac{ \Gamma (p) \Gamma (q) }{ \Gamma (p+q) }\] \[B(p,q) = \frac{ \Gamma (1/4) \Gamma (1/2) }{ \Gamma (1/4+1/2) }\] then i have \[\int\limits\limits\limits_{0}^{\pi/2} (\sin \theta)^{2 (1/4)1} (\cos \theta)^{2 (1/2)1} d \theta = \frac{ 1 }{ 2 } B(p,q)\] \[\int\limits\limits\limits\limits_{0}^{\pi/2} (\sin \theta)^{2 (1/4)1} (\cos \theta)^{2 (1/2)1} d \theta = \frac{ 1 }{ 2 } \frac{ \Gamma(1/4)\Gamma (1/2) }{ \Gamma (1/4+1/2 )}\] finally The solution of gamma and Beta function for \(\int\limits_{0}^{\pi/2} \frac{ d \theta }{ \sqrt{\sin \theta} } \) is \[\frac{ 1 }{ 2 } \frac{ \Gamma (1/4) \Gamma (1/2)}{ \Gamma (\frac{ 1 }{ 4 }+\frac{ 1 }{ 2 }) }\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Oh... okay. You didn't clarify that's what you wanted.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Ok guys actually, i wanna check my work.., hei how about these "find the solution of gamma and beta function for \[\int\limits_{0}^{\pi/2} (\tan^{3}\theta + \tan^{5} \theta) e^{\tan^{2}\theta} d \theta\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0let \(u=\tan^2 \theta\) see what happens, have u tried it yet?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes., i've tried for this one, but it didn't work, oh my bad :(

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0it becomes\[\frac{1}{2}\int_{0}^{\infty} u e^{u} du\]right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0then, \[\frac{ 1 }{ 2 } \int\limits_{0}^{\infty} ue^{u} du = \frac{ 1 }{ 2 } \int\limits_{0}^{\infty} u^{21} e^{u} du\] then p=2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[= \frac{ 1 }{ 2 } \Gamma(2)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and u know that\[\Gamma(n+1)=n!\]we are done :)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ah yeah.., thank you so much @mukushla and other woow we are done :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.