3.6.6 Solving Equations Involving Power Series
LogicalExpand[   ] | give the equations obtained by equating corresponding coefficients in the power series | | | solve for coefficients in 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
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Out[1]=
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| This gives an equation involving the power series. | |
In[2]:=
D[y, x]^2 - y x
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Out[2]=
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| LogicalExpand generates a sequence of equations for each power of x. | |
In[3]:=
LogicalExpand[ % ]
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Out[3]=
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| This solves the equations for the coefficients a[i]. You can also feed equations involving power series directly to Solve. | |
Out[4]=
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Some equations involving power series can also be solved using the InverseSeries function discussed in Section 3.6.4.
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