§14.7 Integer Degree and Order
Contents
- §14.7(i)
- §14.7(ii) Rodrigues-Type Formulas
- §14.7(iii) Reflection Formulas
- §14.7(iv) Generating Functions
§14.7(i)
For ,
14.7.1,
where is the Legendre polynomial of degree . For additional properties of see Chapter 18.
14.7.2
where , and for ,
14.7.3
equivalently,
14.7.4
14.7.5
Next,
14.7.6
where
14.7.7.
§14.7(ii) Rodrigues-Type Formulas
For , and ,
14.7.8
14.7.9
14.7.10
14.7.11
14.7.12
14.7.13
14.7.14
14.7.15
When is even and , and are polynomials of degree . Also,
14.7.16.
§14.7(iii) Reflection Formulas
14.7.17
14.7.18