3.6.6 Solving Equations Involving Power Series

Solving equations involving power series.

Here is a power series.

In[1]:= y = 1 + Sum[a[i] x^i, {i, 3}] + O[x]^4

Out[1]=

This gives an equation involving the power series.

In[2]:= D[y, x]^2 - y == x

Out[2]=

LogicalExpand generates a sequence of equations for each power of x.

In[3]:= LogicalExpand[ % ]

Out[3]=

This solves the equations for the coefficients a[i]. You can also feed equations involving power series directly to Solve.

In[4]:= Solve[ % ]

Out[4]=

Some equations involving power series can also be solved using the InverseSeries function discussed in Section 3.6.4.