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