An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 sider |
Inni boken
Resultat 1-5 av 12
Side 4
... observe , in the first place , that x2 + y2 = r2 sin2 0. Hence V will be independent of p , or will be a function of r and only . The differential equation between r and which it must therefore satisfy will be d2 ( r V ) dr2 + 1 d sin ...
... observe , in the first place , that x2 + y2 = r2 sin2 0. Hence V will be independent of p , or will be a function of r and only . The differential equation between r and which it must therefore satisfy will be d2 ( r V ) dr2 + 1 d sin ...
Side 12
... observing that ( 1 − 2 μ3 + h ” ) + = − 2μh h2 ) 1 - — ( 1 − 2μh + h3 ) + , - dy . = αμ 1 + h αμ 2 + 2 3d ( 12 = 1 ) + 1.32 / ( 2-1 ) + .. · h2 đ2 αμε 2 + . hi 1. 2 idμ 2 ... d ' - + .. .... d ' 1 Hence P1 = P. 2.1.2 · 2 ...
... observing that ( 1 − 2 μ3 + h ” ) + = − 2μh h2 ) 1 - — ( 1 − 2μh + h3 ) + , - dy . = αμ 1 + h αμ 2 + 2 3d ( 12 = 1 ) + 1.32 / ( 2-1 ) + .. · h2 đ2 αμε 2 + . hi 1. 2 idμ 2 ... d ' - + .. .... d ' 1 Hence P1 = P. 2.1.2 · 2 ...
Side 13
... observe that the positive roots of each of these equations are severally equal in absolute mag- nitude to the negative roots . 8. We may take this opportunity of introducing an im- portant theorem , due to Rodrigues , properly belonging ...
... observe that the positive roots of each of these equations are severally equal in absolute mag- nitude to the negative roots . 8. We may take this opportunity of introducing an im- portant theorem , due to Rodrigues , properly belonging ...
Side 19
... observe in the first place that , if m be any 1 integer less than í , С_ ̧μ " P , dμ = 0 . μ " Ραμ For as Pm Pm - 1 ... may all be expressed as rational in- tegral functions of μ , of the degrees m , m - 1 ... respectively , it follows ...
... observe in the first place that , if m be any 1 integer less than í , С_ ̧μ " P , dμ = 0 . μ " Ραμ For as Pm Pm - 1 ... may all be expressed as rational in- tegral functions of μ , of the degrees m , m - 1 ... respectively , it follows ...
Side 29
... observing that 1 − 2 cos Oh + h2 = ( 1 — he√ − 1o ) ( 1 — he − √ — 10 ) , we obtain or ( 1 — he√10 ) 1 ( 1 — he − √ = 10 ) - } = P ̧ + P ̧h + ... + P ̧h ' + ... - - ― 1 . 3 ... ( 2i — 1 ) hie√ = 160 + ... ) 2.4 2i ... ( 1 + 1 ...
... observing that 1 − 2 cos Oh + h2 = ( 1 — he√ − 1o ) ( 1 — he − √ — 10 ) , we obtain or ( 1 — he√10 ) 1 ( 1 — he − √ = 10 ) - } = P ̧ + P ̧h + ... + P ̧h ' + ... - - ― 1 . 3 ... ( 2i — 1 ) hie√ = 160 + ... ) 2.4 2i ... ( 1 + 1 ...
Andre utgaver - Vis alle
An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them Norman Macleod Ferrers Uten tilgangsbegrensning - 1877 |
An Elementary Treatise on Spherical Harmonics, and Subjects Connected with Them Norman M. Ferrers Uten tilgangsbegrensning - 1877 |
An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them N M (Norman MacLeod) 1829-19 Ferrers Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
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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