Commutative algebra Completion and topological rings Concept
Formal power series
Summary
A formal power series is an infinite sum treated as an algebraic object, without any convergence condition. Formal power series form a ring that is the natural home of generating functions. The node formal power series gives the precise definition.
Where this leads
29 pages build on this one.
- Power series solution
- Malgrange preparation theorem
- Horn hypergeometric series
- Symbolic method
- Milnor–Thurston kneading theory
- Weierstrass preparation theorem
- Tate algebra
- Deformation quantization
- Solution of recurrences by generating functions
- Complete local ring
- Frobenius method
- Artin–Mazur zeta function
- Ring of convergent power series
- Kurosh problem
- Lagrange inversion theorem
- Carleman matrix
- Deformation of algebras
- Kontsevich quantization formula
- Multivariate formal power series
- Rogers–Ramanujan identities
- Ruelle zeta function
- Holonomic function
- Symmetric function
- Pentagonal number theorem
- Euler's pentagonal number theorem
- Golod–Shafarevich theorem
- Mather's stability theorem
- Bürmann–Lagrange series
- Kontsevich formality theorem
Further reading
- Web https://en.wikipedia.org/wiki/Formal_power_series, Definition of the formal power series ring
About this page
| Tag | 033WGN00BF |
|---|---|
| URI | m2://033WGN00BF |
| Kind | concept |
| Writing | W1 stated |
| MSC | 13F25 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (1 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Power series solution
- Horn hypergeometric series
- Symbolic method
- Milnor–Thurston kneading theory
- Weierstrass preparation theorem
- Tate algebra
- Deformation quantization
- Solution of recurrences by generating functions
- Complete local ring
- Artin–Mazur zeta function
- Lagrange inversion theorem
- Carleman matrix
- Deformation of algebras
- Kontsevich quantization formula
- Multivariate formal power series
- Rogers–Ramanujan identities
- Ruelle zeta function
- Holonomic function
- Symmetric function
- Pentagonal number theorem
- Euler's pentagonal number theorem
- Golod–Shafarevich theorem