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In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be applied. The Laurent series was named after and first published by Pierre Alphonse Laurent in 1843. Karl Weierstrass may have discovered it first in a paper written in 1841, but it was not published until after his death.
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Wikipedia
Mathematics
field of study
Forwarded from ریاضیات مهندسی (NaCm)
Forwarded from ریاضیات مهندسی (NaCm)
Forwarded from ریاضیات مهندسی (NaCm)
1. A periodic function is defined as:
Anonymous Quiz
11%
f(x+P)=2f(x)
70%
f(x+nP)=f(x)
10%
f(x)=-f(x)
9%
f(x)=f(-x)
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2. The particular conditions that a function f(x) must fulfill in order that it may be expanded as a Fourier series is:
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Gibbs phenomenon
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Fourier-Mellin Theorem
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Dirichlet conditions
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Convolution theorem
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At a point of finite discontinuity, the Fourier series converges to:
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a_m pi
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(1/2)* lim [f(x_0+c)+ f(x_0-c)] when c tends to zero
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f(x_0)
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f(x)=a_0 + a_1 cos(x)