An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 páginas |
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Página 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 ...
Página 20
... determine A ,, A¡ -..... Then , multiplying successively by μ - 2 , μ and inte- ... grating from 1 to +1 , we obtain the following system of equations : - A1 Ai - 2 + ... 2i - 1 2i - 3 + + A1 - 28 2i - 28-1 ... + = 0 , A1 Ai - 2 + 2i35 ...
... determine A ,, A¡ -..... Then , multiplying successively by μ - 2 , μ and inte- ... grating from 1 to +1 , we obtain the following system of equations : - A1 Ai - 2 + ... 2i - 1 2i - 3 + + A1 - 28 2i - 28-1 ... + = 0 , A1 Ai - 2 + 2i35 ...
Página 31
... determine the factor independent of m , we may pro- ceed as follows : PC , cos i0 + C12 cos ( i - 2 ) 0 + ... ; 1 .. P , cos me = √ C , { cos ( m + i ) 0 + cos ( m − i ) 0 } 2 + 1/2 C12 { 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 .. P , cos me = √ C , { cos ( m + i ) 0 + cos ( m − i ) 0 } 2 + 1/2 C12 { cos ( m + i − 2 ) 0 + cos ( m − i + 2 ) 0 } ...
Página 37
... determine this expression , assume dP . άμ ! = C12 P12 + C12 PL3 + ... + CmPm + ... i - 1 i - 1 i - 3 i - 3 then multiplying by P , and integrating with respect to μ from 1 to +1 , And 1 [ Pd , dp = C. f . Pdp = m 2 C'm 2 + 1 w [ PdP1 d ...
... determine this expression , assume dP . άμ ! = C12 P12 + C12 PL3 + ... + CmPm + ... i - 1 i - 1 i - 3 i - 3 then multiplying by P , and integrating with respect to μ from 1 to +1 , And 1 [ Pd , dp = C. f . Pdp = m 2 C'm 2 + 1 w [ PdP1 d ...
Página 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 . Now let O be the centre of the ...
... 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 . Now let O be the centre of the ...
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An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them N M (Norman MacLeod) 1829-19 Ferrers Sin vista previa disponible - 2015 |
Términos y frases comunes
A. S. WALPOLE A. W. VERRALL Assistant Master Assistant-Master axis BEGINNERS BOOK Cambridge centre Classical Clifton College coefficients cos² Crown 8vo degree denoted density Edited by E. S. Edited by Rev ELEMENTARY English Exercises expression external point Extra fcap Fcap Fellow of St Fellow of Trinity Globe 8vo GRAMMAR Hence Illustrations internal Introduction and Notes J. P. MAHAFFY JOHN BOND John's College late Fellow LATIN Lecturer Litt LL.D numerous obtain Owens College Oxford P₁ P₂ plane potential preparation PRIMER radius rational integral function revised and enlarged satisfies the equation School Second Edition sin² solid solid harmonic sphere spherical harmonic suppose surface harmonic Tesseral Translated TREATISE Trinity College University V₁ Vocabulary y+b² y+c² zonal harmonics αμ αμσ µ² µ³
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