proposition 9.95 The two ladder identities
open in the book ·
parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3749
· p. 316
Rests on
- depends_on definition 9.93 Bessel functions of the first kind ¶
- proves proof ch:07-odes-sturm-liouville@proof-45 ¶
Supports
-
depends_on
corollary 9.96
Recurrence relations
¶
- depends_on proposition 9.103 The positive zeros and their spacing ¶
-
depends_on
theorem 9.98
Orthogonality of the Bessel functions
¶
- depends_on proposition 9.100 Fourier–Bessel coefficients ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Bessel functions of the first kind | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3758 |
depends_on |
← | Recurrence relations | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3794 |
proves |
← | ch:07-odes-sturm-liouville@proof-45 | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3761 |