Meaning of Taylor series | Babel Free
Definitions
A power series representation of given infinitely differentiable function f whose terms are calculated from the function's arbitrary order derivatives at given reference point a; the series f(a)+(f'(a))/(1!)(x-a)+(f(a))/(2!)(x-a)²+(f'(a))/(3!)(x-a)³+⋯=∑ₙ₌₀∞(f⁽ⁿ⁾(a))/(n!)(x-a)ⁿ.
Equivalents
Bosanski
Taylorov red
Dansk
Taylorrække
Deutsch
Taylorreihe
Español
serie de Taylor
Suomi
Taylorin sarja
Français
série de Taylor
Hrvatski
Taylorov red
Italiano
serie di Taylor
Português
série de Taylor
Română
serie Taylor
Русский
ряд Те́йлора
Српски
Taylorov red
Examples
“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.”
“The usual procedure for deriving finite-difference equations consists of approximating the derivatives in the differential equation via a truncated Taylor series.”
“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.”
CEFR level
B2
Upper Intermediate
This word is part of the CEFR B2 vocabulary — upper intermediate level.
This word is part of the CEFR B2 vocabulary — upper intermediate level.
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