# Associated Legendre Polynomial

**URL:** <https://community.wolfram.com/t/associated-legendre-polynomial/5502>\
**Category:** Questions\
**Tags:** earth-science, engineering, optics, physics, mathematica, calculus\
**Created:** [April 22, 2015, 6:40am UTC](https://community.wolfram.com/t/associated-legendre-polynomial/5502 "2015-04-22T06:40:43Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![daipayansarkar](https://avatars.discourse-cdn.com/v4/letter/d/8baadc/32.png) [@daipayansarkar](https://community.wolfram.com/u/daipayansarkar)\
**Post date:** [April 22, 2015, 6:40am UTC](https://community.wolfram.com/t/associated-legendre-polynomial/5502/1 "2015-04-22T06:40:43Z")

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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

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**Author:** ![sblinder](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/sblinder/32/17861_2.png) [@sblinder](https://community.wolfram.com/u/sblinder)\
**Post date:** [April 22, 2015, 5:31pm UTC](https://community.wolfram.com/t/associated-legendre-polynomial/5502/2 "2015-04-22T17:31:09Z")

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