An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 Seiten |
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Seite 1
... corresponds another , of the degree - ( i + 1 ) , where r2 = x2 + y2 + z2 . expressed by Vi pi + 1 : For the equation ( 1 ) when transformed to polar co - ordi- nates by writing xr sin cos 0 , y = r sin 0 sin p , z = r cos 0 , becomes 2 ...
... corresponds another , of the degree - ( i + 1 ) , where r2 = x2 + y2 + z2 . expressed by Vi pi + 1 : For the equation ( 1 ) when transformed to polar co - ordi- nates by writing xr sin cos 0 , y = r sin 0 sin p , z = r cos 0 , becomes 2 ...
Seite 14
... corresponding term in ( I ) and of those factors only . Two such terms may be said to be complementary to each other . ... ... 9 . Now , conceive a term in ( II ) the product of p factors of the form x + a , say x + a ' , x + a " x + a ...
... corresponding term in ( I ) and of those factors only . Two such terms may be said to be complementary to each other . ... ... 9 . Now , conceive a term in ( II ) the product of p factors of the form x + a , say x + a ' , x + a " x + a ...
Seite 15
... corresponding term in ( I ) will be , as shewn above , ( x + a ' ) ( x + a ' ) ... ( x + a ( 2 ) ) ( x + B ) ( x + B ,, ) ... ( x + Buy ) ) ( x + , α ) ( x + x ) ... ( x + m2 ) ( x + , ẞ ) ( x + , ẞ ) ( x + mB ) . 1 2 ... Hence ...
... corresponding term in ( I ) will be , as shewn above , ( x + a ' ) ( x + a ' ) ... ( x + a ( 2 ) ) ( x + B ) ( x + B ,, ) ... ( x + Buy ) ) ( x + , α ) ( x + x ) ... ( x + m2 ) ( x + , ẞ ) ( x + , ẞ ) ( x + mB ) . 1 2 ... Hence ...
Seite 25
... correspond- ing factors in the numerator . The power of 2 , in the denominator of P1 , is that which enters as a ... corresponding to these limits are equal and opposite . Hence , ( m + i being even ) m 1 μ TM P1.dμ = 2 [ 2 f ' μm P ...
... correspond- ing factors in the numerator . The power of 2 , in the denominator of P1 , is that which enters as a ... corresponding to these limits are equal and opposite . Hence , ( m + i being even ) m 1 μ TM P1.dμ = 2 [ 2 f ' μm P ...
Seite 47
... corresponding value for any other point , which can be reached without passing through any portion of the attracting mass , will be 1 - π 0 - 3. We may next shew how to obtain , in terms of a series of zonal harmonics , an expression ...
... corresponding value for any other point , which can be reached without passing through any portion of the attracting mass , will be 1 - π 0 - 3. We may next shew how to obtain , in terms of a series of zonal harmonics , an expression ...
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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
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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