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It might not be obvious that these series build up oscillating functions like signs and cosines, but you can again (taking the experimentalist's approach to maths) see it happen on a calculator, or in this animation showing how the sine function builds up as you add more and more terms in the series above: It starts with y = x, a straight line.
Sarason in [17] studied the space of slowly oscillating functions.
The thermal fluctuations are still oscillating functions even in the long-time limit.
Periods of oscillating functions in larger foraminifera may point to tidal, lunar and seasonal cycles.
Discrete G-norm: Meyer [2] has proposed a space G of continuous functions to measure oscillating functions (texture and noise).
We characterize asymptotic dimension (for spaces of finite asymptotic dimension) in terms of extensions of slowly oscillating functions to spheres.
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For example, selecting one DOF and a sine oscillating function would generate a tadpole motion in a 2D plane.
It is true for slowly oscillating continuous functions ([56], Theorem 12), and quasi-slowly oscillating continuous functions ([7], Theorem 3.5), (see also [59], Theorem 5).
The maths we use to understand quantum tunnelling involves connecting oscillating trigonometric functions to exponentials, via imaginary numbers, and plugging it all into Schrödinger's equation.
For the kernel functions in the synaptic coupling, pure excitations, lateral inhibition, the lateral excitations and more general synaptic couplings (e.g., oscillating kernel functions) are considered.
First the grid spacing in the position variable is made coarser by using oscillating interpolation functions derived from the WKB asymptotics.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com