proposition 9.118 The construction solves the associated equation
open in the book ·
parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4549
· p. 325
Rests on
-
depends_on
definition 9.116
Associated Legendre functions
¶
- depends_on definition 9.108 Rodrigues formula ¶
-
depends_on
lemma 9.117
The differentiated Legendre equation
¶
- depends_on equation 9.146 eq:slt-legendre-ode ¶
- proves proof ch:07-odes-sturm-liouville@proof-59 ¶
- proves proof ch:07-odes-sturm-liouville@proof-60 ¶
Supports
-
depends_on
theorem 9.119
Orthogonality at fixed order
¶
- depends_on theorem 9.122 Normalisation and orthonormality ¶
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 |
→ | Associated Legendre functions | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4553 |
depends_on |
→ | The differentiated Legendre equation | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4553 |
depends_on |
← | Orthogonality at fixed order | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4593 |
proves |
← | ch:07-odes-sturm-liouville@proof-60 | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4556 |