An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 sider |
Inni boken
Resultat 1-5 av 15
Side 6
... shewn that the most general solution of equation ( 2 ) of the form of a rational integral function of u involves but one arbitrary constant , and that as a 6 ZONAL HARMONICS . Investigation of expression for P; in terms of u, by ...
... shewn that the most general solution of equation ( 2 ) of the form of a rational integral function of u involves but one arbitrary constant , and that as a 6 ZONAL HARMONICS . Investigation of expression for P; in terms of u, by ...
Side 8
... shewn as 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 ...
... shewn as 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 ...
Side 10
... shewn that , if h be less than 1 , ( 1 − P ̧ + P ̧h + · 2μh + h2 ) − = P ̧ + P ̧h + ... + P ̧h ' + ... If h be greater than 1 , this series becomes divergent . But we may write ( h2 — 2μh + 1 ) −1 = } = 1 ( Po + f ++ .. + fit ...
... shewn that , if h be less than 1 , ( 1 − P ̧ + P ̧h + · 2μh + h2 ) − = P ̧ + P ̧h + ... + P ̧h ' + ... If h be greater than 1 , this series becomes divergent . But we may write ( h2 — 2μh + 1 ) −1 = } = 1 ( Po + f ++ .. + fit ...
Side 13
... shewn that the values of μ , which satisfy the equation P , Ö , are all real , and all lie between 1 and 1 . - For the equation d = ( -1 ) = 0 has i roots = 1 , and i roots = −1 , ..du ( u2 - 1 ) ' = 0 has i - 1 roots = 1 , ( i - 1 ) ...
... shewn that the values of μ , which satisfy the equation P , Ö , are all real , and all lie between 1 and 1 . - For the equation d = ( -1 ) = 0 has i roots = 1 , and i roots = −1 , ..du ( u2 - 1 ) ' = 0 has i - 1 roots = 1 , ( i - 1 ) ...
Side 15
... 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 , the sum of these two terms of ( I ) ...
... 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 , the sum of these two terms of ( I ) ...
Andre utgaver - Vis alle
An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them Norman Macleod Ferrers Uten tilgangsbegrensning - 1877 |
An Elementary Treatise on Spherical Harmonics, and Subjects Connected with Them Norman M. Ferrers Uten tilgangsbegrensning - 1877 |
An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them N M (Norman MacLeod) 1829-19 Ferrers Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
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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