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Complex Analysis -Markushevich's book1 Prob 9.5, 9.6: Root of order k of a polynomial
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Загружено: 2026-01-23
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Описание:
Theory of Functions of a Complex Variable (Vol 1) - A.I. Markushevich
I.9: Elementary Entire Functions
35: Polynomials
36: The mapping w = Pn(z)
37: The Mapping w = (z - a)^n
Prob 9.5: Prove that a necessary and sufficient condition for z = a to be a zero of order k of the polynomial f(z) is that
f(a) = f'(a) = ... = F^{(k-1)}(a) = 0, f^{(k)}(a) is not 0.
Prob 9.6: Prove that if z = a + ib is a zero of order k of the polynomial f(z) with real coefficients, then z* = a - ib is also a zero of order k of f(z).
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