theorem 9.70 Asymptotics of the Airy functions
open in the book ·
parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2410
· p. 301
Rests on
- depends_on definition 9.68 Airy functions ¶
-
depends_on
proposition 9.69
The integral solves the Airy equation
¶
- depends_on definition 9.68 Airy functions ¶ ↺
- depends_on equation 9.76 eq:slt-wkb-airy-equation ¶
- proves proof ch:07-odes-sturm-liouville@proof-35 ¶
- proves proof ch:07-odes-sturm-liouville@proof-36 ¶
Supports
-
depends_on
proposition 23.57
The wave resolution at a turning surface
¶
- depends_on remark 23.58 The caustics that are not turning surfaces ¶
- depends_on remark 23.59 What is observed ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Airy functions | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2429 |
depends_on |
→ | The integral solves the Airy equation | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2429 |
depends_on |
← | The wave resolution at a turning surface | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1945 |
proves |
← | ch:07-odes-sturm-liouville@proof-36 | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2432 |