spherical harmonic

Summary

spherical harmonic is a special function^[1]. It ranks in the top 9% of special_function entities by monthly Wikipedia readership (1,101 views/month).^[2]

Key Facts

• spherical harmonic's image is recorded as Spherical Harmonics.png^[3].
• spherical harmonic's instance of is recorded as special function^[4].
• spherical harmonic's Commons category is recorded as Spherical harmonics^[5].
• spherical harmonic's Freebase ID is recorded as /m/01cv1m^[6].
• spherical harmonic's described by source is recorded as ISO 80000-2:2019 Quantities and units — Part 2: Mathematics^[7].
• spherical harmonic's described by source is recorded as Encyclopædia Britannica 11th edition^[8].
• spherical harmonic's Encyclopædia Britannica Online ID is recorded as topic/spherical-harmonic^[9].
• spherical harmonic's defining formula is recorded as \mathrm{Y}_l^m(\vartheta, \varphi) = \sqrt{\frac{2 l + 1}{4 \pi} \frac{(l - |m|)!}{(l + |m|)!}} \mathrm{P}_l^{|m|}(\cos{\vartheta}) e^{\mathrm{i} m \varphi}, l, |m| \in \boldsymbol{\mathsf{N}}, |m| \leq l^[10].
• spherical harmonic's MathWorld ID is recorded as SphericalHarmonic^[11].
• spherical harmonic's Great Russian Encyclopedia Online ID is recorded as 4175938^[12].
• spherical harmonic's JSTOR topic ID is recorded as spherical-harmonics^[13].
• spherical harmonic's maintained by WikiProject is recorded as WikiProject Mathematics^[14].
• spherical harmonic's Microsoft Academic ID is recorded as 3768446^[15].
• spherical harmonic's Brilliant Wiki ID is recorded as spherical-harmonics^[16].
• spherical harmonic's in defining formula is recorded as \mathrm{Y}_l^m(\vartheta, \varphi)^[17].
• spherical harmonic's in defining formula is recorded as \mathrm{P}_n^m(z)^[18].
• spherical harmonic's in defining formula is recorded as \boldsymbol{\mathsf{N}}^[19].
• spherical harmonic's Encyclopedia of Mathematics article ID is recorded as Spherical_harmonics^[20].
• spherical harmonic's OpenAlex ID is recorded as C3768446^[21].
• spherical harmonic's ScienceDirect topic ID is recorded as computer-science/spherical-harmonic^[22].
• spherical harmonic's ScienceDirect topic ID is recorded as mathematics/spherical-harmonic^[23].
• spherical harmonic's ScienceDirect topic ID is recorded as psychology/spherical-harmonic^[24].
• spherical harmonic's ScienceDirect topic ID is recorded as computer-science/spherical-harmonic-function^[25].
• spherical harmonic's Encyclopedia of China is recorded as 152118^[26].

Why It Matters

spherical harmonic ranks in the top 9% of special_function entities by monthly Wikipedia readership (1,101 views/month).^[2] It has Wikipedia articles in 21 language editions, a strong signal of global cultural recognition.^[27] It is known by 31 alternative names across languages and contexts.^[28]