Solution Found!
Evaluate (Hint: Change variables to convert the integrand
Chapter , Problem 8P(choose chapter or problem)
Evaluate \(\Gamma\left(\frac{1}{2}\right)\) (Hint: Change variables to convert the integrand to a Gaussian.) Then use the recursion formula to evaluate \(\Gamma\left(\frac{3}{2}\right) \text { and } \Gamma\left(-\frac{1}{2}\right)\).
Figure B.3. The gamma function, \(\Gamma(n)\). For positive integer arguments, \(\Gamma(n)\) = (n-1)!. For positive nonintegers, \(\Gamma(n)\) can be computed from equation B.12, while for negative nonintegers, \(\Gamma(n)\)can be computed from equation B.14.
Questions & Answers
QUESTION:
Evaluate \(\Gamma\left(\frac{1}{2}\right)\) (Hint: Change variables to convert the integrand to a Gaussian.) Then use the recursion formula to evaluate \(\Gamma\left(\frac{3}{2}\right) \text { and } \Gamma\left(-\frac{1}{2}\right)\).
Figure B.3. The gamma function, \(\Gamma(n)\). For positive integer arguments, \(\Gamma(n)\) = (n-1)!. For positive nonintegers, \(\Gamma(n)\) can be computed from equation B.12, while for negative nonintegers, \(\Gamma(n)\)can be computed from equation B.14.
ANSWER:To evaluate
Step 1:
For the positive values of , the Gamma function
=
----(1)
Evaluating for =