Treatise of Physics

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theorem 9.133 Orthonormality

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:5107 · p. 331

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theorem 9.133: Orthonormality9.133equation 9.175: eq:slt-laguerre-data9.175proposition 9.131: Explicit form and generating function9.131theorem 9.57: Orthogonality of Sturm–Liouville eigenfunctions9.57proposition 9.134: Laguerre series9.134proof : ch:07-odes-sturm-liouville@proof-71proofdefinition 9.130: Laguerre polynomials9.130proposition 9.132: The equation and the recurrence9.132proof : ch:07-odes-sturm-liouville@proof-69proofequation 9.55: eq:slt-eigenproblem9.55lemma 9.56: Lagrange identity9.56phenomenon 28.53: Chladni's figures28.53phenomenon 28.45: The harmonic series of a stretched string28.45theorem 9.119: Orthogonality at fixed order9.119theorem 9.98: Orthogonality of the Bessel functions9.98theorem 9.127: Orthogonality9.127theorem 9.111: Orthogonality of the Legendre polynomials9.111proof : ch:07-odes-sturm-liouville@proof-29proofdefinition 9.47: Orthonormal series expansion9.47proof : ch:07-odes-sturm-liouville@proof-72proof

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typedirectionnode provenancewhere
depends_on → eq:slt-laguerre-data declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:5113
depends_on → Explicit form and generating function declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:5113
depends_on → Orthogonality of Sturm–Liouville eigenfunctions declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:5113
depends_on ← Laguerre series declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:5147
proves ← ch:07-odes-sturm-liouville@proof-71 declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:5117