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powseries[powcreate] - create formal power series

Calling Sequence

powcreate(eqns)

Parameters

eqns

-

expression sequence of equations

Description

• 

The function powcreate creates a formal power series whose coefficients are specified by eqns.

• 

The expression sequence of equations passed to powcreate should consist of one equation, possibly recursive, that specifies the nth coefficient, followed by zero or more equations that specify initial conditions.

• 

More specifically, powcreate(t(n)=expr, t(0)=a0, ..., t(m)=am) creates a formal power series, t, whose nth coefficient is expr, and whose initial terms are t0=a0, ..., tm=am.

• 

Any initial conditions among eqns override the general expression.  Thus, it is possible to include particular values of coefficients in eqns.

• 

The command with(powseries,powcreate) allows the use of the abbreviated form of this command.

Examples

withpowseries:

powcreatetn=1n!,t0=1:

tpsformt,x,7

1+x+12x2+16x3+124x4+1120x5+1720x6+Ox7

(1)

powcreatevn=vn1+vn24,v0=4,v1=2:

tpsformv,x

4+2x+32x2+78x3+1932x4+47128x5+Ox6

(2)

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