theorem 9.113 Generating function

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4371 · p. 323

Rests on

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 ¶

Supports

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 ¶

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`	→	The polynomial solution is unique up to scale	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4379
`depends_on`	→	Rodrigues' polynomials solve the equation	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4379
`depends_on`	←	MacCullagh's formula	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:690
`depends_on`	←	Recurrence relations	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4433
`proves`	←	ch:07-odes-sturm-liouville@proof-56	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4383