Legendre function
solutions of Legendre's differential equation
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Legendre function
Summary
Legendre function ranks in the top 2% of general entities by monthly Wikipedia readership (93 views/month).[1]
Key Facts
- Legendre function's GND ID is recorded as 4332825-8[2].
- Legendre function's Library of Congress authority ID is recorded as sh85075778[3].
- Legendre function's Bibliothèque nationale de France ID is recorded as 12259775t[4].
- Legendre function's IdRef ID is recorded as 031369499[5].
- Legendre function's subclass of is recorded as special function[6].
- Legendre function's subclass of is recorded as mathematical concept[7].
- Legendre function's Freebase ID is recorded as /m/0bwhl6d[8].
- Legendre function's National Library of Spain SpMaBN ID is recorded as XX536155[9].
- Legendre function's different from is recorded as Legendre polynomial[10].
- Legendre function's different from is recorded as Legendre chi function[11].
- Legendre function's FAST ID is recorded as 995590[12].
- Legendre function's defining formula is recorded as P_{\lambda}^{\mu}(z) = \frac{1}{\Gamma(1-\mu)} \left[\frac{1+z}{1-z}\right]^{\mu/2} \,_2F_1 \left(-\lambda, \lambda+1; 1-\mu; \frac{1-z}{2}\right),\qquad \text{for } \ |1-z|<2[13].
- Legendre function's defining formula is recorded as Q_{\lambda}^{\mu}(z) = \frac{\sqrt{\pi}\ \Gamma(\lambda+\mu+1)}{2^{\lambda+1}\Gamma(\lambda+3/2)}\frac{e^{i\mu\pi}(z^2-1)^{\mu/2}}{z^{\lambda+\mu+1}} \,_2F_1 \left(\frac{\lambda+\mu+1}{2}, \frac{\lambda+\mu+2}{2}; \lambda+\frac{3}{2}; \frac{1}{z^2}\right),\qquad \text{for}\ \ |z|>1[14].
- Legendre function's JSTOR topic ID is recorded as legendre-functions[15].
- Legendre function's maintained by WikiProject is recorded as WikiProject Mathematics[16].
- Legendre function's Microsoft Academic ID is recorded as 153262748[17].
- Legendre function's National Library of Israel J9U ID is recorded as 987007560402605171[18].
- Legendre function's OpenAlex ID is recorded as C153262748[19].
- Legendre function's Yale LUX ID is recorded as concept/24ef0893-c63e-4f5f-b4c3-89b4755c0697[20].
Why It Matters
Legendre function ranks in the top 2% of general entities by monthly Wikipedia readership (93 views/month).[1]