Editing Legendre function (section)

===Positive integer order ===
For positive integer <math> \mu = m \in \N^+ </math> the evaluation of <math> P^\mu_\lambda </math> above involves cancellation of singular terms. We can find the limit valid for <math> m \in \N_0 </math> as<ref>{{cite journal | url=https://www.degruyter.com/document/doi/10.1515/mcma-2018-0001/html?lang=de | doi=10.1515/mcma-2018-0001 | title=Fast generation of isotropic Gaussian random fields on the sphere | date=2018 | last1=Creasey | first1=Peter E. | last2=Lang | first2=Annika | journal=Monte Carlo Methods and Applications | volume=24 | issue=1 | pages=1–11 | arxiv=1709.10314 | bibcode=2018MCMA...24....1C | s2cid=4657044 }}</ref>

<math display="block">P^m_\lambda(z) = \lim_{\mu \to m} P^\mu_\lambda (z) = \frac{(-\lambda )_m (\lambda + 1)_m}{m!} \left[\frac{1-z}{1+z}\right]^{m/2} \,_2F_1 \left(-\lambda, \lambda+1; 1+m; \frac{1-z}{2}\right), </math>

with <math>(\lambda)_{n}</math> the (rising) [[Pochhammer symbol]].