Differential Equations › Section F · Series solutions › Topic F.5
Special functions in applications
Series solutions of a few important equations come up so often that they have names, tables and software, just like sine and cosine. Knowing their key properties lets you use them as confidently as any familiar function.
In this topic
- Named solutions
- Legendre polynomials
- Worked example: P₂ from a stopping series
- Worked example: building P₃ by recurrence
- Generating functions and multipoles
- Orthogonality and Gaussian quadrature
- Hermite and Laguerre polynomials
- Bessel functions in practice
- Truncated series as approximations
- Common mistakes to avoid
- Key takeaways
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