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Exercise [07.03] b
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Joined: 07 Jun 2008, 08:21
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Exercise [07.03] b
This is what I think Penrose wants you to do:

Taylor's expansion for about the point is:

Also Cauchy's formula in the origin shifted form is:

Show that is indeed given by:

I am about to substitute the Taylor series for f(z) given above into the contour integral without worrying about the rigorous justification, which is what Penrose suggests you do in the exercise:

and now a further step without rigorous justification

and then expanding the summation

Using the result of exercise 7.1 that when is an integer other than we can see that the above simplifies to

since see RTR book section 7.2

which was to be shown.

13 Jul 2008, 16:18
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