Differential Equations › Section F · Series solutions › Topic F.4
The Frobenius method
At many singular points the solutions behave like a power of x, as Euler equations showed, but with a power series attached. The Frobenius method finds that power and that series, and it is the standard route to the series for Bessel functions.
In this topic
- A power times a series
- Regular and irregular singular points
- The Frobenius form
- The indicial equation
- Worked example: setting up 2xy″ + y′ + y = 0
- Worked example: the two solutions
- Three cases for the roots
- Worked example: roots one apart, no logarithm
- Bessel's equation
- Common mistakes to avoid
- Key takeaways
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