theorem 9.127 Orthogonality

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4910 · p. 329

Rests on

depends_on equation 9.167 eq:slt-hermite-data ¶
depends_on proposition 9.126 Recurrence relations and the equation ¶
- depends_on equation 9.166 eq:slt-hermite-ode ¶
- depends_on proposition 9.125 Generating function and first properties ¶
  - depends_on definition 9.124 Hermite polynomials ¶
  - proves proof ch:07-odes-sturm-liouville@proof-65 ¶
- proves proof ch:07-odes-sturm-liouville@proof-66 ¶
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-67 ¶

Supports

depends_on proposition 9.128 Hermite series ¶

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`	→	eq:slt-hermite-data	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4915
`depends_on`	→	Recurrence relations and the equation	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4915
`depends_on`	→	Orthogonality of Sturm–Liouville eigenfunctions	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4915
`depends_on`	←	Hermite series	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4953
`proves`	←	ch:07-odes-sturm-liouville@proof-67	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4919