proposition 9.100 Fourier–Bessel coefficients

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3930 · p. 318

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depends_on definition 9.47 Orthonormal series expansion ¶
- depends_on definition 9.45 Orthonormal set of functions ¶
depends_on theorem 9.98 Orthogonality of the Bessel functions ¶
- depends_on corollary 9.96 Recurrence relations ¶
  - depends_on proposition 9.95 The two ladder identities ¶
    - depends_on definition 9.93 Bessel functions of the first kind ¶
    - proves proof ch:07-odes-sturm-liouville@proof-45 ¶
  - proves proof ch:07-odes-sturm-liouville@proof-46 ¶
- depends_on equation 9.132 eq:slt-bessel-scaled ¶
- 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-47 ¶
proves proof ch:07-odes-sturm-liouville@proof-49 ¶

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type	direction	node	provenance	where
`depends_on`	→	Orthonormal series expansion	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3943
`depends_on`	→	Orthogonality of the Bessel functions	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3943
`proves`	←	ch:07-odes-sturm-liouville@proof-49	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3946