Taylor series
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See also: Taylorseries
English[edit]
Alternative forms[edit]
Etymology[edit]
Named after English mathematician Brook Taylor, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician James Gregory.
Noun[edit]
Taylor series (plural Taylor series)
- (calculus) A power series representation of given infinitely differentiable function whose terms are calculated from the function's arbitrary order derivatives at given reference point ; the series .
- 1978, [McGraw-Hill], Carl M. Bender, Steven A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Springer, published 1999, page 324:
- A series solution about an ordinary point of a differential equation is always a Taylor series having a nonvanishing radius of convergence. A series solution about a singular point does not have this form (except in rare cases). Instead, it may be either a convergent series not in Taylor series form (such as a Frobenius series) or it may be a divergent series.
- 1980, Suhas Patankar, Numerical Heat Transfer and Fluid Flow[1], Taylor & Francis (CRC Press), page 28:
- The usual procedure for deriving finite-difference equations consists of approximating the derivatives in the differential equation via a truncated Taylor series.
- 1998, Kenneth L. Judd, Numerical Methods in Economics, The MIT Press, page 197:
- This function has its only singularity at x = 0, implying that the radius of convergence for the Taylor series around x = 1 is only unity.
Hyponyms[edit]
- (power series of a function calculated from derivatives at a reference point): Maclaurin series
Translations[edit]
power series of a function calculated from derivatives at a reference point
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