Solution Found!
Show that by writing by making the transformation y =
Chapter 4, Problem 196SE(choose chapter or problem)
Show that \(\Gamma(1 / 2)=\sqrt{\pi}\) by writing
\(\Gamma(1/2)=\int_0^{\infty}y^{-1/2}e^{-y}\ dy\)
by making the transformation \(y=(1 / 2) x^{2}\) and by employing the result of Exercise 4.194.
Equation Transcription:
Text Transcription:
(1/2)=sqrt pi
(1/2)=integral 0 to infinity y^-1/2 e^-y dy
y=(1/2)x^2
Questions & Answers
QUESTION:
Show that \(\Gamma(1 / 2)=\sqrt{\pi}\) by writing
\(\Gamma(1/2)=\int_0^{\infty}y^{-1/2}e^{-y}\ dy\)
by making the transformation \(y=(1 / 2) x^{2}\) and by employing the result of Exercise 4.194.
Equation Transcription:
Text Transcription:
(1/2)=sqrt pi
(1/2)=integral 0 to infinity y^-1/2 e^-y dy
y=(1/2)x^2
ANSWER:
Solution:
Step 1 of 1:
To show that
Where,
Then, differentiate ‘y’, we get