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Expansion

Taylor series, theta series, Pade series, and generalized series

MuPAD Functions

asympt Compute an asymptotic series expansion
mtaylor Compute a multivariate Taylor series expansion
O Domain of order terms (Landau symbols)
ORDER Default number of terms in series expansions
pade Pade approximation
series Compute a generalized series expansion
taylor Compute a Taylor series expansion

MuPAD Domains

Series::Puiseux Truncated Puiseux series expansions
Series::gseries Generalized series expansions

Examples and How To

Compute Taylor Series for Univariate Expressions

Taylor series expansions serve for approximating an arbitrary expression by a polynomial expression around some value of a variable.

Compute Taylor Series for Multivariate Expressions

To compute a series expansion for a multivariate expression, use the mtaylor command.

Control Number of Terms in Series Expansions

Taylor series expansions approximate an arbitrary expression with a polynomial.

Compute Generalized Series

The Taylor series expansion is the most common way to approximate an expression by a polynomial.

Concepts

O-term (The Landau Symbol)

When computing the series expansions, you get expressions with one of the terms represented as the Landau symbol O.

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