proposition 9.109 Rodrigues' polynomials solve the equation

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4217 · p. 321

Rests on

depends_on lemma 9.110 The polynomial solution is unique up to scale ¶
- depends_on theorem 9.113 Generating function ¶
  - depends_on proposition 29.24 MacCullagh's formula ¶
    - depends_on phenomenon 29.49 Precession of the equinoxes ¶
      - depends_on proposition 29.50 The principal nutation ¶
  - depends_on proposition 9.114 Recurrence relations ¶
    - depends_on proposition 9.120 Recurrence in the degree at fixed order ¶
depends_on theorem 9.113 Generating function ¶ ↺
depends_on theorem 9.111 Orthogonality of the Legendre polynomials ¶
- depends_on proposition 9.115 Legendre series ¶
- depends_on theorem 9.119 Orthogonality at fixed order ¶
  - depends_on theorem 9.122 Normalisation and orthonormality ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Rodrigues formula	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4223
`depends_on`	→	eq:slt-legendre-ode	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4223
`depends_on`	←	The polynomial solution is unique up to scale	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4264
`depends_on`	←	Generating function	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4379
`depends_on`	←	Orthogonality of the Legendre polynomials	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4294
`proves`	←	ch:07-odes-sturm-liouville@proof-53	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4226