Associated Legendre Polynomial

Questions
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1

Hello,

I am curious to learn how Mathematica computes the value of an Associated Legendre Polynomial (ALP) with half-integer order and integer degree. For the case of integer degree and order, ALP can be expressed explicitly using the formula as listed in the help section of LegendreP[n,m,x] and can be found in the Mathematica documentation (ref/LegendreP).

Is there an explicit way of defining ALP with integer degree and half integer order?.

Thanks in advance.

Best Regards,

D. Sarkar

2

Express the APL in terms of Gauss hypergeometric function. Parameters can be non integer. For explicit formulas, see, for example, Abramowitz & Stegun.