Help with partial fractions.
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Help with partial fractions.

[From: ] [author: ] [Date: 11-06-15] [Hit: ]
ab = r² and a + b = 2r.0 = b² - 2rb + r² = (b - r)² ==> b = r.Similarly a = r.It doesnt matter if r is pure real.Are you sure your original expression is 1/(z - r)² as opposed to 1/(z² - r²)?Perhaps you are not aware that 1/(z - r)² is its own partial fraction decomposition.......
I need to re-express the term,

(z - r)^(-2)
so one over (z - r) squared, where r is a positive real number and z is a complex variable.

into multiple fractions of the form:

A(z - a)^(-1) + B(z - b)^(-1) where a and b are complex numbers and neither equals r, and A and B are functions of z.

Please help?

-
Uhhh... this requires

ab = r² and a + b = 2r.

A little substitution leads to the equation

0 = b² - 2rb + r² = (b - r)² ==> b = r.

Similarly a = r. It doesn't matter if r is pure real.

Are you sure your original expression is 1/(z - r)² as opposed to 1/(z² - r²)?

Perhaps you are not aware that 1/(z - r)² is its own "partial fraction decomposition".
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