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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 sequence often can be limited to a finite numer of terms, thus yielding an approximation of the function. The fewer terms of the seuence are used, the simpler this approach will be. Often, the resulting inaccuracy (i.e., the partial sum of the omitted terms) can be described by am equation.

There are several kinds of series expansions, such as:

• Taylor series
• Maclaurin series: A special case of a Taylor series.
• Laurent series: An extension of the Taylor series, allowing negative exponent values.
• 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.
• Legendre polynomials: Used in physics to describe an arbitrary electrical field as a superposition of a dipole filed, 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.

Category:Algebra Category:Polynomials Category:Mathematical analysis Category:Mathematical series