proposition 9.128 Hermite series

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4945 · p. 330

Rests on

depends_on definition 9.47 Orthonormal series expansion ¶
- depends_on definition 9.45 Orthonormal set of functions ¶
depends_on theorem 9.127 Orthogonality ¶
- 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 ¶
proves proof ch:07-odes-sturm-liouville@proof-68 ¶

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type	direction	node	provenance	where
`depends_on`	→	Orthonormal series expansion	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4953
`depends_on`	→	Orthogonality	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4953
`proves`	←	ch:07-odes-sturm-liouville@proof-68	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4956