An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 Seiten |
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Seite 1
... obtained . in finite terms . We can , however , 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 ...
... obtained . in finite terms . We can , however , 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 ...
Seite 2
... obtained from U by multiplying by 1 Such an expression as V , we shall call a Solid Spherical Harmonic of the degree . The result obtained by dividing V by r , which will be a function of two inde- pendent variables and only , we shall ...
... obtained from U by multiplying by 1 Such an expression as V , we shall call a Solid Spherical Harmonic of the degree . The result obtained by dividing V by r , which will be a function of two inde- pendent variables and only , we shall ...
Seite 6
... obtain , for the most general form of ƒ ( μ ) , αμ ƒ ( μ ) = CP1 + C , P1 √ P2 ( 1 - 42 ) . - Now , P. being a rational integral function of μ of i i dimensions , it may be seen that - du ( 1 − μ3 ) P ̧2 will assume the form of the ...
... obtain , for the most general form of ƒ ( μ ) , αμ ƒ ( μ ) = CP1 + C , P1 √ P2 ( 1 - 42 ) . - Now , P. being a rational integral function of μ of i i dimensions , it may be seen that - du ( 1 − μ3 ) P ̧2 will assume the form of the ...
Seite 14
... obtained will consist of an equal number of terms , and to any term in ( I ) will corre- spond one term in ( II ) , such that their product will be ( x + α ̧ ) ( x + α2 ) ( x + α1 ) ( x + B1 ) ( x + ẞ ̧ ) ... .. ( x + B1 ) , i.e. the ...
... obtained will consist of an equal number of terms , and to any term in ( I ) will corre- spond one term in ( II ) , such that their product will be ( x + α ̧ ) ( x + α2 ) ( x + α1 ) ( x + B1 ) ( x + ẞ ̧ ) ... .. ( x + B1 ) , i.e. the ...
Seite 16
... 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.
... 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
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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