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powseries

  

reversion

  

reversion of formal power series

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

reversion(a, b)

Parameters

a

-

formal power series

b

-

(optional) formal power series

Description

• 

The function reversion(a, b) returns the formal power series that is the reversion of a with respect to b.  If b is not specified then it is assumed to be the formal power series with one nonzero coefficient, b1=1.

• 

Since reversion is the inverse of composition, composition of the result into a will give b.

• 

Note that a0 must be 0, a1 must be 1, and b0 must be 0. If not, the reversion is not well defined and reversion returns an error message.

• 

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

Examples

withpowseries:

powcreatetn=tn1n,t0=0,t1=1:

powcreatevn=vn12,v0=0,v1=1:

sreversiont,v:

tpsforms,x,11

x+112x3+180x5+1448x7+12304x9+Ox11

(1)

tscomposet,s:

tpsformts,x

x+12x2+14x3+18x4+116x5+Ox6

(2)

tpsformv,x

x+12x2+14x3+18x4+116x5+Ox6

(3)

See Also

solve[series]

 


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