equation 9.146 eq:slt-legendre-ode
open in the book ·
parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4196
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Supports
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depends_on
lemma 9.117
The differentiated Legendre equation
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depends_on
proposition 9.118
The construction solves the associated equation
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depends_on
theorem 9.119
Orthogonality at fixed order
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- depends_on theorem 9.122 Normalisation and orthonormality ¶
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depends_on
theorem 9.119
Orthogonality at fixed order
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depends_on
proposition 9.118
The construction solves the associated equation
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depends_on
proposition 9.109
Rodrigues' polynomials solve the equation
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depends_on
lemma 9.110
The polynomial solution is unique up to scale
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depends_on
theorem 9.113
Generating function
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depends_on
proposition 29.24
MacCullagh's formula
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- depends_on phenomenon 29.49 Precession of the equinoxes ¶
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depends_on
proposition 9.114
Recurrence relations
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- depends_on proposition 9.120 Recurrence in the degree at fixed order ¶
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depends_on
proposition 29.24
MacCullagh's formula
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depends_on
theorem 9.113
Generating function
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- depends_on theorem 9.113 Generating function ¶ ↺
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depends_on
theorem 9.111
Orthogonality of the Legendre polynomials
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- depends_on proposition 9.115 Legendre series ¶
- depends_on theorem 9.119 Orthogonality at fixed order ¶ ↺
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depends_on
lemma 9.110
The polynomial solution is unique up to scale
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| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
← | The differentiated Legendre equation | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4533 |
depends_on |
← | Rodrigues' polynomials solve the equation | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:4223 |