proposition 9.115 Legendre series

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4459 · p. 324

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depends_on definition 9.47 Orthonormal series expansion ¶
- depends_on definition 9.45 Orthonormal set of functions ¶
depends_on theorem 9.111 Orthogonality of the Legendre polynomials ¶
- 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 ¶
- depends_on theorem 9.57 Orthogonality of Sturm–Liouville eigenfunctions ¶
  - depends_on equation 9.55 eq:slt-eigenproblem ¶
  - depends_on lemma 9.56 Lagrange identity ¶
    - depends_on definition 9.54 Sturm–Liouville differential operator ¶
    - proves proof ch:07-odes-sturm-liouville@proof-28 ¶
  - proves proof ch:07-odes-sturm-liouville@proof-29 ¶
- proves proof ch:07-odes-sturm-liouville@proof-55 ¶
proves proof ch:07-odes-sturm-liouville@proof-58 ¶

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type	direction	node	provenance	where
`depends_on`	→	Orthonormal series expansion	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4468
`depends_on`	→	Orthogonality of the Legendre polynomials	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4468
`proves`	←	ch:07-odes-sturm-liouville@proof-58	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4471