power series
- noun
- /ˈpaʊər ˈsɪriz/
- Specialized
:
serie de potencias
- To evaluate the function near zero, we can use a power series expansion that includes terms up to x cubed.
Examples
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To compute the trace, we expand the logarithm in an infinite power series.
Academic text (2018) -
This is approximately equal for small epsilon, but the exact formula is a power series in epsilon.
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So this would be the power series representation for our function.
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And that would be our power series representation.
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You understand if you have a graph that is a power series in Y, if it begins with Y square it will look like this.
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In calculus, a power series can represent functions such as e^x as an infinite sum of terms that involve increasing powers of x.
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The power series for sin(x) converges for all real numbers, allowing for its use in solving differential equations.
Surface Forms
Morphology
The phrase is directly compositional: 'series' means a sum and 'power' refers to exponents, so a learner who knows both words can infer it is a sum made up of powers (i.e. terms with increasing exponents). This construction is cross-linguistically common (e.g. Spanish 'serie de potencias'), so the core meaning is predictable though some technical details (infinite, variable) are mathematical rather than lexical.
Etymology
The term power series comes from a simple image: it is a series, a long sum, made of rising powers of a letter like x, for example x, x², x³. Picture a row of terms getting taller and all added together, and you can see why power series means 'a sum made from higher and higher powers of a variable'.
