An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them |
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Page ix
Norman Macleod Ferrers. CHAPTER IV . SPHERICAL HARMONICS IN GENERAL . TESSERAL AND SECTORIAL HARMONICS . ZONAL ... harmonic of the degree i will involve 2i + 1 arbi- trary constants • 5. Derivation of successive harmonics from the zonal ...
Norman Macleod Ferrers. CHAPTER IV . SPHERICAL HARMONICS IN GENERAL . TESSERAL AND SECTORIAL HARMONICS . ZONAL ... harmonic of the degree i will involve 2i + 1 arbi- trary constants • 5. Derivation of successive harmonics from the zonal ...
Page 2
... Spherical Harmonic of the degree . The result obtained by dividing V by r , which will be a function of two inde- pendent variables and only , we shall call a Surface Spherical Harmonic of the same degree . A very important form of ...
... Spherical Harmonic of the degree . The result obtained by dividing V by r , which will be a function of two inde- pendent variables and only , we shall call a Surface Spherical Harmonic of the same degree . A very important form of ...
Page 3
... Zonal Harmonics , and designates all other spherical harmonics by the name of Laplace's Functions . The Zonal Harmonic in the case which we shall consider in the following chapter , i.e. , in which the system is symmetrical about the ...
... Zonal Harmonics , and designates all other spherical harmonics by the name of Laplace's Functions . The Zonal Harmonic in the case which we shall consider in the following chapter , i.e. , in which the system is symmetrical about the ...
Page 4
Norman Macleod Ferrers. CHAPTER II . ZONAL HARMONICS . 1. WE shall in this chapter regard a Zonal Solid Har- monic , of the degree i , as a homogeneous function of ... spherical harmonic of the degree i will involve 2i+1 arbi- trary ...
Norman Macleod Ferrers. CHAPTER II . ZONAL HARMONICS . 1. WE shall in this chapter regard a Zonal Solid Har- monic , of the degree i , as a homogeneous function of ... spherical harmonic of the degree i will involve 2i+1 arbi- trary ...
Page 5
... Zonal Harmonics ; and the point in which the positive direction of the axis meets a sphere whose centre is the origin of co - ordinates , and radius unity , is called the Pole of the system . Any constant multiple of a zonal harmonic ...
... Zonal Harmonics ; and the point in which the positive direction of the axis meets a sphere whose centre is the origin of co - ordinates , and radius unity , is called the Pole of the system . Any constant multiple of a zonal harmonic ...
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Common terms and phrases
Assistant-Master axis b²+w become infinite bounding surface C₁ Cambridge centre Chap co-ordinates coefficients component attraction confocal ellipsoid corresponding cos² Crown 8vo degree denoted distance dV dV dy dz Edited by Rev ellipsoidal harmonics equal Eton College expression external point Extra fcap factor fcap Fellow of St follows Greek Hence homogeneous function internal John's College lamina late Fellow LATIN monics multiplying numerous obtain Oxford P₁ P₂ plane positive integer potential Professor radius rational integral function satisfies the equation series of zonal shewn sin² solid angle solid harmonic solutions sphere spherical harmonic spherical shell suppose surface harmonic Tesseral thickness Trinity College V₁ writing y+b² y+c² zonal harmonics αμ αμσ µ² µ³ µ³)³ προ
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