associated Legendre polynomials

Summary

associated Legendre polynomials is a Legendre function^[1]. It draws 171 Wikipedia views per month (legendre_function category, ranking #1 of 1).^[2]

Key Facts

• associated Legendre polynomials's image is recorded as Mplwp legendreP04a0.svg^[3].
• associated Legendre polynomials's image is recorded as Mplwp legendreP15a1.svg^[4].
• associated Legendre polynomials's image is recorded as Mplwp legendreP26a2.svg^[5].
• associated Legendre polynomials's instance of is recorded as Legendre function^[6].
• associated Legendre polynomials's instance of is recorded as mathematical concept^[7].
• Adrien-Marie Legendre is named after associated Legendre polynomials^[8].
• associated Legendre polynomials's GND ID is recorded as 4333224-9^[9].
• associated Legendre polynomials's subclass of is recorded as special function^[10].
• associated Legendre polynomials's subclass of is recorded as function^[11].
• associated Legendre polynomials's Freebase ID is recorded as /m/042nzg^[12].
• associated Legendre polynomials's described by source is recorded as ISO 80000-2:2019 Quantities and units — Part 2: Mathematics^[13].
• associated Legendre polynomials's different from is recorded as Legendre polynomial^[14].
• associated Legendre polynomials's defining formula is recorded as \mathrm{P}_n^m(z) = (-1)^m (1 - z^2)^{m/2} \frac{\mathrm{d}^m}{\mathrm{d}z^m} \mathrm{P}_n(z), m, n \in \boldsymbol{\mathsf{N}}, m \leq n^[15].
• associated Legendre polynomials's MathWorld ID is recorded as AssociatedLegendrePolynomial^[16].
• associated Legendre polynomials's maintained by WikiProject is recorded as WikiProject Mathematics^[17].
• associated Legendre polynomials's Microsoft Academic ID is recorded as 36956377^[18].
• associated Legendre polynomials's ProofWiki ID is recorded as Associated_Legendre_Function^[19].
• associated Legendre polynomials's in defining formula is recorded as \mathrm{P}_n^m(z)^[20].
• associated Legendre polynomials's in defining formula is recorded as \mathrm{P}_n(z)^[21].
• associated Legendre polynomials's in defining formula is recorded as \boldsymbol{\mathsf{N}}^[22].
• associated Legendre polynomials's OpenAlex ID is recorded as C36956377^[23].
• associated Legendre polynomials's ScienceDirect topic ID is recorded as mathematics/associated-legendre-function^[24].

Why It Matters

associated Legendre polynomials draws 171 Wikipedia views per month (legendre_function category, ranking #1 of 1).^[2] It has Wikipedia articles in 15 language editions, a strong signal of global cultural recognition.^[25] It is known by 13 alternative names across languages and contexts.^[26]