An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 sider |
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Resultat 1-5 av 18
Side 9
... proceed as follows : If p , be the coefficient of h ' in the expansion of H , H = 1 + ph + ph + ... + ph + . .. hH = h + p ̧h2 + P ̧h3 + + p ̧hi + 1 + ... ... d2 : . h dh2 ( hH ) = 1.2p , h + 2.3p , h2 + + i ( i + 1 ) p ; h ' + ...
... proceed as follows : If p , be the coefficient of h ' in the expansion of H , H = 1 + ph + ph + ... + ph + . .. hH = h + p ̧h2 + P ̧h3 + + p ̧hi + 1 + ... ... d2 : . h dh2 ( hH ) = 1.2p , h + 2.3p , h2 + + i ( i + 1 ) p ; h ' + ...
Side 11
... in the result putting = μ . Both these methods how- r ever would be somewhat laborious ; we proceed therefore to investigate more convenient expressions . 6. The first process shews , by the aid of ZONAL HARMONICS . 11 PAGE.
... in the result putting = μ . Both these methods how- r ever would be somewhat laborious ; we proceed therefore to investigate more convenient expressions . 6. The first process shews , by the aid of ZONAL HARMONICS . 11 PAGE.
Side 14
... proceed to calculate the other factor . For this purpose consider the expression ( x + α ̧ ) ( x + α2 ) ... ( x + α1 ) ( x + ẞ ̧ ) ( x + B2 ) ... ( x + ß . ) . Conceive this differentiated ( I ) im times , ( II ) i + m times . The two ...
... proceed to calculate the other factor . For this purpose consider the expression ( x + α ̧ ) ( x + α2 ) ... ( x + α1 ) ( x + ẞ ̧ ) ( x + B2 ) ... ( x + ß . ) . Conceive this differentiated ( I ) im times , ( II ) i + m times . The two ...
Side 25
... proceed to investigate the value of if m have any other value . For this purpose , resuming the notation of the equations of Art . 13 , we see that , putting 0 = m + 1 , and ∞ = ∞ , we have X1-2 a , + m + 1 a1-2 + m + 1 = X1 Xi - 28 + ...
... proceed to investigate the value of if m have any other value . For this purpose , resuming the notation of the equations of Art . 13 , we see that , putting 0 = m + 1 , and ∞ = ∞ , we have X1-2 a , + m + 1 a1-2 + m + 1 = X1 Xi - 28 + ...
Side 26
... proceed to shew . Suppose that m is a positive integer , and that μm is de- veloped in such a series , the coefficient of P , being C , so that μm = = ΣC , P .; i then , multiplying both sides of this equation by P , and inte- grating ...
... proceed to shew . Suppose that m is a positive integer , and that μm is de- veloped in such a series , the coefficient of P , being C , so that μm = = ΣC , P .; i then , multiplying both sides of this equation by P , and inte- grating ...
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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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