“Variation of Argument”的概念、定义、习题解题方法及翻译-数学辞典

单词

Variation of Argument

释义

Variation of Argument

Let denote the change in argument of a function around a closed loop . Also let denotethe number of Roots of in and denote the number of Poles of in. Then

(1)

To find

in a given region

, break

into paths and find

for each path. On a circularArc

(2)

let

be a Polynomial

of degree

. Then


			(3)

Plugging in

gives

(4)

(5)

(6)

and

(7)

For a Real segment

(8)

For an Imaginary segment

(9)

Note that the Argument must change continuously, so ``jumps'' occur across inverse tangent asymptotes.

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