coeftayl - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Power Series : coeftayl

coeftayl

coefficient of (multivariate) expression

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

coeftayl(expr, eqn, k)

Parameters

expr

-

arbitrary expression

eqn

-

equation of the form x=α where x is a name (univariate case) or list (multivariate case)

k

-

non-negative integer (univariate case) or a list of non-negative integers (multivariate case)

Description

• 

This function computes a coefficient in the (multivariate) Taylor series representation of expr without forming the series (it uses differentiation and substitution).  Often, expr is a polynomial.

• 

The one-variable and several-variable cases are distinguished by the types of the input parameters.

• 

UNIVARIATE CASE: x is a name and k a non-negative integer.

  

In this case, the value returned is the coefficient of xαk in the Taylor series expansion of expr about x=α.  This is equivalent to executing  coefftaylorexpr,x=α,k+1,xα,k  but it is more efficient (because only a single term is computed).

• 

MULTIVARIATE CASE: x is a nonempty list x1,,xv of indeterminates appearing in expr and α is a list α1,,αv specifying the point of expansion with respect to the given indeterminates;  k is a list k1,,kv of non-negative integers corresponding to elements in x and α.

  

In this case, the value returned is the coefficient of the term specified by the monomial

  

 

x1α1k1xvαvkv

  

in the multivariate Taylor series expansion of expr about the point x=α.  If k is the list of zeros then the value returned is the value resulting from substituting x=α into expr.

Examples

p2x2+3y35

p:=3y3+2x25

(1)

coeftaylp,x=0,2

2

(2)

coeftaylp,x=1,1

4

(3)

taylorp,x=1

3y33+4x1+2x12

(4)

q3ax+12+sinax2yy2x+xa

q:=3ax+12+sinax2yy2x+xa

(5)

coeftaylq,x=1,2

3a+sinay

(6)

coeftaylq,x=1,1

12sinayy2

(7)

taylorq,x=1

sinay+y21a+12sinayy2x+1+3a+sinayx+12

(8)

coeftaylq,x,y=0,0,0,0

2a

(9)

coeftaylq,x,y=0,0,2,1

sina

(10)

mtaylorq,x,y

2a+6a+1x+3ax2+sinax2yy2x

(11)

coeftaylq,x,y=0,1,1,1

2

(12)

coeftaylq,x,y=0,1,2,1

sina

(13)

mtaylorq,x=0,y=1

2a+6ax+sina+3ax22y1x+sinax2y1y12x

(14)

See Also

coeff

coeffs

mtaylor

taylor

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam