An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 Seiten |
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Ergebnisse 1-5 von 27
Seite 1
... determine an expression which we shall call V , an homogeneous function of x , y , z of the degree i , i being any positive integer , which will satisfy the equation ; and we may prove that to every such solution V , there corresponds ...
... determine an expression which we shall call V , an homogeneous function of x , y , z of the degree i , i being any positive integer , which will satisfy the equation ; and we may prove that to every such solution V , there corresponds ...
Seite 20
... determine A ,, A - 9 .... i - 2 i - 4 Then , multiplying successively by μ , μ , ... and inte- grating from 1 to +1 , we obtain the following system of equations : - A A - 2 A - 20 + ... + + + = ... 0 , 2i - 1 2i - 3 2i - 2s -1 A , A i ...
... determine A ,, A - 9 .... i - 2 i - 4 Then , multiplying successively by μ , μ , ... and inte- grating from 1 to +1 , we obtain the following system of equations : - A A - 2 A - 20 + ... + + + = ... 0 , 2i - 1 2i - 3 2i - 2s -1 A , A i ...
Seite 31
... determine the factor independent of m , we may pro- ceed as follows : PC , cos i0 + C12 cos ( i - 2 ) 0 + ... ; 1 2 .. P , cos me = 1⁄2 C , { cos ( m + i ) 0. + cos ( m − i ) 0 } + 11⁄2 С12 { cos ( m + i − 2 ) 0 + cos ( m − i + 2 ) 0 } ...
... determine the factor independent of m , we may pro- ceed as follows : PC , cos i0 + C12 cos ( i - 2 ) 0 + ... ; 1 2 .. P , cos me = 1⁄2 C , { cos ( m + i ) 0. + cos ( m − i ) 0 } + 11⁄2 С12 { cos ( m + i − 2 ) 0 + cos ( m − i + 2 ) 0 } ...
Seite 37
... determine this expression , assume dP . = C12 P12 + C1s PLs + ... + CmPm + ... άμ i - 1 then multiplying by Pm , and integrating with respect to μ from 1 to +1 , - And 1 L dP m du = C άμ dP1 m 1 2 Pdu = C'm 2m + 1 i άμ dPm dμl . [ Pd dp ...
... determine this expression , assume dP . = C12 P12 + C1s PLs + ... + CmPm + ... άμ i - 1 then multiplying by Pm , and integrating with respect to μ from 1 to +1 , - And 1 L dP m du = C άμ dP1 m 1 2 Pdu = C'm 2m + 1 i άμ dPm dμl . [ Pd dp ...
Seite 48
... determining the solid angle which it subtends at any point of a line . drawn through its centre perpendicular to its plane , and then deducing the general expression by the employment of zonal harmonics . = 0 . Hence is itself a ...
... determining the solid angle which it subtends at any point of a line . drawn through its centre perpendicular to its plane , and then deducing the general expression by the employment of zonal harmonics . = 0 . Hence is itself a ...
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An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them N M (Norman MacLeod) 1829-19 Ferrers Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
a²+v Assistant-Master axis become infinite bounding surface c²+v Cambridge centre Chap co-ordinates coefficients confocal ellipsoid cos² Crown 8vo degree denoted dx² dµdp 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 P₁₂ 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 V₂ writing y+b² y+c² Y₁ zonal harmonics αμ αμσ µ² µ³ προ
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