proposition 9.120 Recurrence in the degree at fixed order

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4647 · p. 326

Rests on

depends_on definition 9.116 Associated Legendre functions ¶
- depends_on definition 9.108 Rodrigues formula ¶
depends_on proposition 9.114 Recurrence relations ¶
- depends_on theorem 9.113 Generating function ¶
  - depends_on lemma 9.110 The polynomial solution is unique up to scale ¶
    - depends_on proposition 9.109 Rodrigues' polynomials solve the equation ¶
      - depends_on definition 9.108 Rodrigues formula ¶ ↺
      - depends_on equation 9.146 eq:slt-legendre-ode ¶
      - proves proof ch:07-odes-sturm-liouville@proof-53 ¶
    - proves proof ch:07-odes-sturm-liouville@proof-54 ¶
  - depends_on proposition 9.109 Rodrigues' polynomials solve the equation ¶ ↺
  - proves proof ch:07-odes-sturm-liouville@proof-56 ¶
- proves proof ch:07-odes-sturm-liouville@proof-57 ¶
proves proof ch:07-odes-sturm-liouville@proof-62 ¶

Supports

Nothing declares a dependency on this node yet.

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:4654
`depends_on`	→	Recurrence relations	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4654
`proves`	←	ch:07-odes-sturm-liouville@proof-62	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4657