Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
experimentX
Group Title
Prove:
\[ \Gamma(z)\Gamma(1z) = \frac{\pi}{\sin{(\pi z)}} \]
 2 years ago
 2 years ago
experimentX Group Title
Prove: \[ \Gamma(z)\Gamma(1z) = \frac{\pi}{\sin{(\pi z)}} \]
 2 years ago
 2 years ago

This Question is Closed

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349012805707:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349012926410:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
this is Euler's reflection formula ... http://en.wikipedia.org/wiki/Reflection_formula I never tried this. Looks worth!!
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.0
\[\displaystyle \sin(\pi z) = \pi z \prod_{n \neq 0} \left(1 \frac zn\right) \exp\left( \frac z n \right)\]
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
beta function\[B(x,y)=\frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\]so\[\Gamma(z)\Gamma(1z)=B(z,1z)=\int_{0}^{\infty} \frac{u^{z1}}{1+u} \text{d}u\]
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
later integral can be done complex integration on this dw:1349016144043:dwcontour
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
thats a circle i believe...lol
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
this contour will work i know...but there are some more
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
dw:1349016381131:dw
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.0
\[\displaystyle \frac 1 {\Gamma \left({z}\right)} = z e^{\gamma z} \prod_{n=1}^\infty \left({ 1 + \frac z n}\right) \exp\left({\frac z n}\right)\]
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
yeah i can do that contour!!
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
that must be equal to ... directly from the formula \[ \pi \over \sin (\pi z)\] \[ \int_0^{\infty}{x^{a1} \over {1 +x^b}}dx = {\pi \over b \sin \left ( {a \pi \over b} \right )} \]
 2 years ago
See more questions >>>
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.