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theorem 9.57 Orthogonality of Sturm–Liouville eigenfunctions

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:1939 · p. 295

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theorem 9.57: Orthogonality of Sturm–Liouville eigenfunctions9.57equation 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 9.133: Orthonormality9.133theorem 9.111: Orthogonality of the Legendre polynomials9.111proof : ch:07-odes-sturm-liouville@proof-29proofdefinition 9.54: Sturm–Liouville differential operator9.54lemma A.442: The Wronskian of the accessory equation is constantA.442proof : ch:07-odes-sturm-liouville@proof-28proofproposition 10.29: Time separation reduces the canonical equations to Helmholtz10.29proof : ch:11-oscillations-waves@proof-29proofequation 28.46: eq:osc-wave-eq28.46proof : ch:11-oscillations-waves@proof-24proofproposition 9.118: The construction solves the associated equation9.118theorem 9.122: Normalisation and orthonormality9.122proof : ch:07-odes-sturm-liouville@proof-61proofcorollary 9.96: Recurrence relations9.96equation 9.132: eq:slt-bessel-scaled9.132proposition 9.100: Fourier–Bessel coefficients9.100proof : ch:07-odes-sturm-liouville@proof-47proofequation 9.167: eq:slt-hermite-data9.167proposition 9.126: Recurrence relations and the equation9.126proposition 9.128: Hermite series9.128proof : ch:07-odes-sturm-liouville@proof-67proofequation 9.175: eq:slt-laguerre-data9.175proposition 9.131: Explicit form and generating function9.131proposition 9.134: Laguerre series9.134proof : ch:07-odes-sturm-liouville@proof-71proofproposition 9.109: Rodrigues' polynomials solve the equation9.109proposition 9.115: Legendre series9.115proof : ch:07-odes-sturm-liouville@proof-55proof

Edges

typedirectionnode provenancewhere
depends_on → eq:slt-eigenproblem declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:1952
depends_on → Lagrange identity declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:1952
depends_on ← Chladni's figures declared parts/03-classical-mechanics/11-oscillations-waves.tex:1932
depends_on ← The harmonic series of a stretched string declared parts/03-classical-mechanics/11-oscillations-waves.tex:1593
depends_on ← Orthogonality at fixed order declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4593
depends_on ← Orthogonality of the Bessel functions declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3844
depends_on ← Orthogonality declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4915
depends_on ← Orthonormality declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:5113
depends_on ← Orthogonality of the Legendre polynomials declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4294
proves ← ch:07-odes-sturm-liouville@proof-29 declared parts/02-mathematical-methods/07-odes-sturm-liouville.tex:1955