Probability and complex function: Unit IV: Complex integration
Singularities - residues residue theorem
Complex integration
If a function f (z) is analytic in a region R, is zero at a point z = z0 in R, then z0 is called a zero of f (z).
SINGULARITIES - RESIDUES RESIDUE THEOREM
1. Singularities - Classification
(a)
Zeros of an Analytic function :
If
a function f (z) is analytic in a region R, is zero at a point z = z0
in R, then z0 is called a zero of f (z).
(b) Simple zero
If
f (z0) 0 and f' (z0) 0, then z = zo is called a simple
zero of f(z) or a zero of the first order.
(c) Zero of order n
If
f (z0) = f' (z0) = … fn-1 (z0) = 0
and fn (z0) ≠ 0, then z0 is called a zero of
order n.
(or)
An
analytic function f (z) is said to have a zero of order n, if f (z) can be
expressed as f (z) = (z - z0)n p (z) where p (z) is
analytic and (z0) ≠ 0.
Probability and complex function: Unit IV: Complex integration : Tag: : Complex integration - Singularities - residues residue theorem
Related Topics
Related Subjects
Probability and complex function
MA3303 3rd Semester EEE Dept | 2021 Regulation | 3rd Semester EEE Dept 2021 Regulation