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- Series_expansion abstract "In mathematics, a series expansion is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication and division).The resulting so-called series often can be limited to a finite number of terms, thus yielding an approximation of the function. The fewer terms of the sequence are used, the simpler this approximation will be. Often, the resulting inaccuracy (i.e., the partial sum of the omitted terms) can be described by an equation involving Big O notation (see also asymptotic expansion).There are several kinds of series expansions, such as: Taylor series: A power series based on a function’s derivatives at a single point. Maclaurin series: A special case of a Taylor series, centred at zero. Laurent series: An extension of the Taylor series, allowing negative exponent values. Dirichlet series: Used in number theory. Fourier series: Describes periodical functions as a series of sine and cosine functions. In acoustics, e.g., the fundamental tone and the overtones together form an example of a Fourier series. Newtonian series Legendre polynomials: Used in physics to describe an arbitrary electrical field as a superposition of a dipole field, a quadrupole field, an octupole field, etc. Zernike polynomials: Used in optics to calculate aberrations of optical systems. Each term in the series describes a particular type of aberration.For more details, refer to the articles mentioned.".
- Series_expansion wikiPageID "1575813".
- Series_expansion wikiPageLength "1987".
- Series_expansion wikiPageOutDegree "34".
- Series_expansion wikiPageRevisionID "610448183".
- Series_expansion wikiPageWikiLink Acoustics.
- Series_expansion wikiPageWikiLink Approximation.
- Series_expansion wikiPageWikiLink Asymptotic_expansion.
- Series_expansion wikiPageWikiLink Big_O_notation.
- Series_expansion wikiPageWikiLink Category:Algebra.
- Series_expansion wikiPageWikiLink Category:Mathematical_analysis.
- Series_expansion wikiPageWikiLink Category:Mathematical_series.
- Series_expansion wikiPageWikiLink Category:Polynomials.
- Series_expansion wikiPageWikiLink Derivative.
- Series_expansion wikiPageWikiLink Dipole.
- Series_expansion wikiPageWikiLink Dirichlet_series.
- Series_expansion wikiPageWikiLink Fourier_series.
- Series_expansion wikiPageWikiLink Function_(mathematics).
- Series_expansion wikiPageWikiLink Fundamental_frequency.
- Series_expansion wikiPageWikiLink Laurent_series.
- Series_expansion wikiPageWikiLink Legendre_polynomials.
- Series_expansion wikiPageWikiLink Maclaurin_series.
- Series_expansion wikiPageWikiLink Mathematics.
- Series_expansion wikiPageWikiLink Multipole_expansion.
- Series_expansion wikiPageWikiLink Number_theory.
- Series_expansion wikiPageWikiLink Optical_aberration.
- Series_expansion wikiPageWikiLink Optics.
- Series_expansion wikiPageWikiLink Overtone.
- Series_expansion wikiPageWikiLink Partial_sum.
- Series_expansion wikiPageWikiLink Physics.
- Series_expansion wikiPageWikiLink Power_series.
- Series_expansion wikiPageWikiLink Quadrupole.
- Series_expansion wikiPageWikiLink Series_(mathematics).
- Series_expansion wikiPageWikiLink Superposition_principle.
- Series_expansion wikiPageWikiLink Table_of_Newtonian_series.
- Series_expansion wikiPageWikiLink Taylor_series.
- Series_expansion wikiPageWikiLink Trigonometric_functions.
- Series_expansion wikiPageWikiLink Zernike_polynomials.
- Series_expansion wikiPageWikiLinkText "series expansion".
- Series_expansion hasPhotoCollection Series_expansion.
- Series_expansion subject Category:Algebra.
- Series_expansion subject Category:Mathematical_analysis.
- Series_expansion subject Category:Mathematical_series.
- Series_expansion subject Category:Polynomials.
- Series_expansion hypernym Method.
- Series_expansion type Software.
- Series_expansion type Type.
- Series_expansion type Field.
- Series_expansion type Function.
- Series_expansion type Polynomial.
- Series_expansion type Type.
- Series_expansion comment "In mathematics, a series expansion is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication and division).The resulting so-called series often can be limited to a finite number of terms, thus yielding an approximation of the function. The fewer terms of the sequence are used, the simpler this approximation will be.".
- Series_expansion label "Series expansion".
- Series_expansion sameAs Reihenentwicklung.
- Series_expansion sameAs Reeksontwikkeling.
- Series_expansion sameAs m.0gtwsj7.
- Series_expansion sameAs Serieutveckling.
- Series_expansion sameAs Q358733.
- Series_expansion sameAs Q358733.
- Series_expansion wasDerivedFrom Series_expansion?oldid=610448183.
- Series_expansion isPrimaryTopicOf Series_expansion.