definition 9.47 Orthonormal series expansion

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:1669 · p. 291

ground object -- no derivation owed

Rests on

depends_on definition 9.45 Orthonormal set of functions ¶

Supports

depends_on proposition 9.100 Fourier–Bessel coefficients ¶
depends_on proposition 9.48 Expansion coefficients ¶
- depends_on proposition 9.50 Coefficients of a product ¶
  - depends_on proposition 9.52 Product coefficients for the Fourier system ¶
depends_on proposition 9.128 Hermite series ¶
depends_on proposition 9.134 Laguerre series ¶
depends_on proposition 9.115 Legendre 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`	→	Orthonormal set of functions	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:1675
`depends_on`	←	Fourier–Bessel coefficients	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3943
`depends_on`	←	Expansion coefficients	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:1683
`depends_on`	←	Hermite series	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4953
`depends_on`	←	Laguerre series	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:5147
`depends_on`	←	Legendre series	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4468