An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 páginas |
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Página 1
... corresponds another , of the degree - ( i + 1 ) , V1 expressed by where r2 = x2 + y2 + z2 . pli + 1 For the equation ( 1 ) when transformed to polar co - ordi- nates by writing x = r sin cos 0 , y = r sin 0 sin 4 , z = r cos 0 , becomes ...
... corresponds another , of the degree - ( i + 1 ) , V1 expressed by where r2 = x2 + y2 + z2 . pli + 1 For the equation ( 1 ) when transformed to polar co - ordi- nates by writing x = r sin cos 0 , y = r sin 0 sin 4 , z = r cos 0 , becomes ...
Página 14
... corresponding term in ( I ) and of those factors only . Two such terms may be said to be complementary to each other . Now , conceive a term in ( II ) the product of p factors of the form x + a , say x + a ' , x + ά ' ... x + a ( 2 ) ...
... corresponding term in ( I ) and of those factors only . Two such terms may be said to be complementary to each other . Now , conceive a term in ( II ) the product of p factors of the form x + a , say x + a ' , x + ά ' ... x + a ( 2 ) ...
Página 15
... corresponding term in ( I ) will be , as shewn above , ( x + α ) ( x + a ' ) ... ( x + a ( 1 ) ) ( x + ẞ , ) ( x + B ) ... ( x + B1 ) ( x + , α ) ( x + , 2 ) ... ( x + m2 ) ( x + ‚ ß ) ( x + „ B ) ... ( x + „ B ) . 2 2 B ( ) ...
... corresponding term in ( I ) will be , as shewn above , ( x + α ) ( x + a ' ) ... ( x + a ( 1 ) ) ( x + ẞ , ) ( x + B ) ... ( x + B1 ) ( x + , α ) ( x + , 2 ) ... ( x + m2 ) ( x + ‚ ß ) ( x + „ B ) ... ( x + „ B ) . 2 2 B ( ) ...
Página 25
... correspond- ing factors in the numerator . The power of 2 , in the denominator of P , is that which enters as a factor ... corresponding to these limits are equal and opposite . Hence , ( m + i being even ) 1 m 1 [ __ " P ,. dp = 2 [ ' μ ...
... correspond- ing factors in the numerator . The power of 2 , in the denominator of P , is that which enters as a factor ... corresponding to these limits are equal and opposite . Hence , ( m + i being even ) 1 m 1 [ __ " P ,. dp = 2 [ ' μ ...
Página 47
... corresponding value for any other point , which can be reached without passing through any portion of the attracting mass , will be 1 S = [ [ $ { z + ( 22 — r2 ) 1 cos & } d9 . π D } 3. We may next shew how to obtain , in terms of a ...
... corresponding value for any other point , which can be reached without passing through any portion of the attracting mass , will be 1 S = [ [ $ { z + ( 22 — r2 ) 1 cos & } d9 . π D } 3. We may next shew how to obtain , in terms of a ...
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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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