tei'au

valsi

tei'au

type

experimental cmavo

creator

krtisfranks

time entered

Wed Apr 25 04:45:05 2018  

English

Definition #70638 - Preferred

 

selma'o

VUhU

definition

4-ary mekso operator: Taylor expansion/polynomial term; for ordered input MATH

$(X_1, X_2, X_3, X_4)$

(X₁, X₂, X₃, X₄), output is the X₃th Taylor polynomial term of at-least-X₃-smooth function X₂ which was expanded around point X₄ and which is evaluated at point X₁, namely MATH

$(1/(X_3!)) * (D^{X_3}(X_2))(X_4) * (X_1-X_4)^{X_3}$

(1/(X₃!))*(D^X₃(X₂))(X₄)*(X₁ - X₄)^X₃.

notes

All of the usual assumptions must apply in order to be well-defined. X₃ must be a nonnegative integer. X₂ must be a function with at least X₃ derivatives on the interval disc/interval defined by X₁ and X₄ such that said derivative takes values for which the other operators make sense (and finity is usually assumed). X₁ and X₄ must be elements of the domain of X₂ (and the X₃th derivative thereof in the latter case). The notation " MATH

$(D^<a class="undefined" href="../dict/X_3?bg=1;langidarg=2">X_3</a>(X_2))(X_4)$

(D^X₃(X₂))(X₄)" represents the X₃th derivative of X₂, applied to X₄; the "!" notation represents the factorial.

gloss words

• Taylor expansion term
• Taylor polynomial term
• Taylor term

created by

krtisfranks

vote information

1

time

Wed Apr 25 04:47:16 2018

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Examples

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