Analytic function
Summary
An analytic function is a function that is given locally by a convergent power series. Analytic functions are smooth, but not all smooth functions are analytic. The node analytic function gives the precise definition.
Where this leads
16 pages build on this one.
- Holmgren's uniqueness theorem
- Cauchy–Kovalevskaya theorem
- Kneser's construction of real analytic tetration
- Smoothness and analyticity of harmonic functions
- Analytic function between Banach spaces
- Regular singular point
- Diffeology
- Cauchy–Kovalevskaya theorem for ODEs
- Real analytic manifold
- Łojasiewicz inequality
- Shift operator as an exponential of differentiation
- Semianalytic set
- Hilbert's nineteenth problem
- Ordinary point and singular point
- Cartan–Kähler theorem
- Analytic combinatorics
Further reading
- Web https://en.wikipedia.org/wiki/Analytic_function, lead section
About this page
| Tag | 081WKEDK6C |
|---|---|
| URI | m2://081WKEDK6C |
| Kind | concept |
| Writing | W1 stated |
| MSC | 26E05 |
| Specializes | Smooth function |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- Holmgren's uniqueness theorem
- Cauchy–Kovalevskaya theorem
- Kneser's construction of real analytic tetration
- Smoothness and analyticity of harmonic functions
- Analytic function between Banach spaces
- Regular singular point
- Diffeology
- Cauchy–Kovalevskaya theorem for ODEs
- Real analytic manifold
- Łojasiewicz inequality
- Shift operator as an exponential of differentiation
- Semianalytic set
- Hilbert's nineteenth problem
- Ordinary point and singular point
- Cartan–Kähler theorem
- Analytic combinatorics