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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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gptkb:heat_equation
gptkb:signal_processing
acoustics
image analysis
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gptkbp:component
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cosine function
sine function
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gptkbp:convergesTo
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gptkb:Dirichlet
gptkb:Lebesgue
gptkb:Riemann
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gptkbp:definedIn
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an infinite sum of sines and cosines
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gptkbp:field
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gptkb:Mathematics
Fourier analysis
Harmonic analysis
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gptkbp:general_form
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a_0/2 + Σ (a_n cos(nx) + b_n sin(nx))
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gptkbp:property
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periodicity
completeness in L2 space
orthogonality of sine and cosine functions
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gptkbp:relatedTo
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gptkb:Gibbs_phenomenon
gptkb:Parseval's_theorem
gptkb:Fourier_Series
Bessel's inequality
Pointwise convergence
Uniform convergence
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gptkbp:studiedBy
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gptkb:Jean-Baptiste_Joseph_Fourier
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gptkbp:used_in
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gptkb:partial_differential_equations
electrical engineering
quantum mechanics
approximation theory
representation of periodic functions
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gptkbp:bfsParent
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gptkb:Antoni_Zygmund
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gptkbp:bfsLayer
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6
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https://www.w3.org/2000/01/rdf-schema#label
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Trigonometric Series
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