theorem 9.122 Normalisation and orthonormality

Rests on

• depends_on equation 9.109 eq:slt-helmholtz-orthonormality ¶
• depends_on theorem 9.119 Orthogonality at fixed order ¶
  • depends_on proposition 9.118 The construction solves the associated equation ¶
    • depends_on definition 9.116 Associated Legendre functions ¶
      • depends_on definition 9.108 Rodrigues formula ¶
    • depends_on lemma 9.117 The differentiated Legendre equation ¶
      • depends_on equation 9.146 eq:slt-legendre-ode ¶
      • proves proof ch:07-odes-sturm-liouville@proof-59 ¶
    • proves proof ch:07-odes-sturm-liouville@proof-60 ¶
  • depends_on theorem 9.111 Orthogonality of the Legendre polynomials ¶
    • depends_on proposition 9.109 Rodrigues' polynomials solve the equation ¶
      • depends_on definition 9.108 Rodrigues formula ¶ ↺
      • depends_on equation 9.146 eq:slt-legendre-ode ¶ ↺
      • proves proof ch:07-odes-sturm-liouville@proof-53 ¶
    • 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-55 ¶
  • depends_on theorem 9.57 Orthogonality of Sturm–Liouville eigenfunctions ¶ ↺
  • proves proof ch:07-odes-sturm-liouville@proof-61 ¶
• proves proof ch:07-odes-sturm-liouville@proof-64 ¶

Supports

Nothing declares a dependency on this node yet.