I am having trouble with problems from the following book: Mathematical Methods in the Physical Sciences, Third Edition, Mary L. Boas. Specifically, I am looking at problem 11.3.8 and 11.3.9.
The directions state, "Express each of the following integrals as a function.
For #8, the problem is stated
I get based on the definition of the gamma function as defined by the text.
The gamma function is defined as follows in the text,
However, I am not sure if this is correct and is someone willing to verify the answer?
For #9, I am not sure where to begin:
The problem is stated Hint: Put
What am I supposed to do with this? The hint doesn't help me much. I still have to integrate with respect to u and I don't know how to put dx in terms of du if this is the case. Does anyone have any suggestions of where to begin or how to set-up this problem?