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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.