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MultiSeries

  

SeriesInfo

  

return information about a multiseries

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

SeriesInfo[ListCoefficients](S)

SeriesInfo[ListExponents](S)

SeriesInfo[CoefficientBigO](S)

SeriesInfo[ExponentBigO](S)

SeriesInfo[Variable](S)

SeriesInfo[Scale](S)

Parameters

S

-

a multiseries

Description

• 

The SeriesInfo subpackage is a collection of simple procedures that return information about multiseries. They are intended to serve as a programmer interface to the SERIES data structure. For compatibility with future releases, it is strongly recommended that you use these commands instead of accessing the operands of the data structure directly.

• 

The ListCoefficients function returns the list of coefficients of S.

• 

The ListExponents function returns the list of exponents of S.

• 

The CoefficientBigO function returns the coefficient in the O... term of S.

• 

The ExponentBigO function returns the exponent of the variable in the O... term of S.

• 

A multiseries S without an O... term yields CoefficientBigOS=0 and ExponentBigOS=.

• 

The Variable function returns the variable used in the series S.

• 

The Scale function returns the asymptotic scale in which S has been expanded.

Examples

withMultiSeries:

withSeriesInfo:

An example with a simple power series expansion:

smultiseriessinx,x

sxx36+x5120+Ox7

(1)

ListCoefficientss

1,16,1120

(2)

ListExponentss

1,3,5

(3)

CoefficientBigOs

1

(4)

ExponentBigOs

7

(5)

Variables

x

(6)

A more complicated expansion:

SmultiseriesΓx,x=

S2π1x+2π1x3212+2π1x522881392π1x72518405712π1x922488320+1638792π1x112209018880+O1x132ⅇlnx1x

(7)

VariableS

1ⅇlnx1x

(8)

CoefficientBigOS

0

(9)

ExponentBigOS

(10)

listcoeffListCoefficientsS

listcoeff2π1x+2π1x3212+2π1x522881392π1x72518405712π1x922488320+1638792π1x112209018880+O1x132

(11)

Llistcoeff1

L2π1x+2π1x3212+2π1x522881392π1x72518405712π1x922488320+1638792π1x112209018880+O1x132

(12)

typeL,SERIES

true

(13)

VariableL

1x

(14)

ListCoefficientsL

2π,2π12,2π288,1392π51840,5712π2488320,1638792π209018880

(15)

ListExponentsL

12,32,52,72,92,112

(16)

See Also

MultiSeries

MultiSeries[multiseries]

type[SERIES]