An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 Seiten |
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Seite 8
... follows . If x , y , z be the co - ordinates of any point , z the distance of a fixed point , situated on the axis of z , from the origin , and R be the distance between these points , we know that , and that Ra = x2 + y2 + ( z ' — 2 ) ...
... follows . If x , y , z be the co - ordinates of any point , z the distance of a fixed point , situated on the axis of z , from the origin , and R be the distance between these points , we know that , and that Ra = x2 + y2 + ( z ' — 2 ) ...
Seite 9
... 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 ' + ... ... Also , the ...
... 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 ' + ... ... Also , the ...
Seite 13
... follows that d ' i dμ3 ( μ2 — 1 ) ' = 0 has 1/2 i roots between 1 and 0 , and roots be- tween 0 and -1 , if i be ... follows : If m be any integer less than i , di - m dx - m 1.2 ... ( im ) ( x2 - 1 ) = 1.2 ... ( i + m ) • ( x2 - 1 ) m ...
... follows that d ' i dμ3 ( μ2 — 1 ) ' = 0 has 1/2 i roots between 1 and 0 , and roots be- tween 0 and -1 , if i be ... follows : If m be any integer less than i , di - m dx - m 1.2 ... ( im ) ( x2 - 1 ) = 1.2 ... ( i + m ) • ( x2 - 1 ) m ...
Seite 14
... follows that the equation di - m dxi i - m ( x − 1 ) ' = 0 - has i ( im ) roots ( i . e . m ) roots each = 1 , and m roots 1 , in other words that ( x2 - 1 ) " is a factor of each = - di - m dx1 ̄m ( x2 — 1 ) . i - m We proceed to ...
... follows that the equation di - m dxi i - m ( x − 1 ) ' = 0 - has i ( im ) roots ( i . e . m ) roots each = 1 , and m roots 1 , in other words that ( x2 - 1 ) " is a factor of each = - di - m dx1 ̄m ( x2 — 1 ) . i - m We proceed to ...
Seite 16
... now establish two very important proper- ties of the function P ; and apply them to obtain the develop- ment of P in a series . The properties in question are as follows : If i 16 ZONAL HARMONICS . Rodrigues' theorem Proof that Proof that.
... now establish two very important proper- ties of the function P ; and apply them to obtain the develop- ment of P in a series . The properties in question are as follows : If i 16 ZONAL HARMONICS . Rodrigues' theorem Proof that Proof that.
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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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