An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 Seiten |
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Seite 1
... positive integer , which will satisfy the equation ; and we may prove that to every such solution V , there corresponds another , of the degree - ( i + 1 ) , where r2 = x2 + y2 + z2 . expressed by Vi pi + 1 : For the equation ( 1 ) when ...
... positive integer , which will satisfy the equation ; and we may prove that to every such solution V , there corresponds another , of the degree - ( i + 1 ) , where r2 = x2 + y2 + z2 . expressed by Vi pi + 1 : For the equation ( 1 ) when ...
Seite 5
... positive direction of the axis meets a sphere whose centre is the origin of co - ordinates , and radius unity , is called the Pole of the system . Any constant multiple of a zonal harmonic ( solid or surface ) is itself a zonal harmonic ...
... positive direction of the axis meets a sphere whose centre is the origin of co - ordinates , and radius unity , is called the Pole of the system . Any constant multiple of a zonal harmonic ( solid or surface ) is itself a zonal harmonic ...
Seite 13
... positive roots of each of these equations are severally equal in absolute mag- nitude to the negative roots . 8. We may take this opportunity of introducing an im- portant theorem , due to Rodrigues , properly belonging to the ...
... positive roots of each of these equations are severally equal in absolute mag- nitude to the negative roots . 8. We may take this opportunity of introducing an im- portant theorem , due to Rodrigues , properly belonging to the ...
Seite 17
... positive integers , [ P.Pdμ = 0 . And fpap = 2i + 1 The following is a proof of the first property . We have d du { ( 1 − μ3 ) dP - αμς + i ( i + 1 ) P ̧ = 0 , d dP m - + m ( m + 1 ) Pm = 0 . 2 Multiplying the first of these equations ...
... positive integers , [ P.Pdμ = 0 . And fpap = 2i + 1 The following is a proof of the first property . We have d du { ( 1 − μ3 ) dP - αμς + i ( i + 1 ) P ̧ = 0 , d dP m - + m ( m + 1 ) Pm = 0 . 2 Multiplying the first of these equations ...
Seite 18
... positive integers . Hence we need only discuss the case in which m = i . We may remark , however , that since P1 = P_ ( 4 ) the determination of the value of Pd will also P = P_ - ( i + 1 ) 9 give the value of The value of ( 1 − 2μh + ...
... positive integers . Hence we need only discuss the case in which m = i . We may remark , however , that since P1 = P_ ( 4 ) the determination of the value of Pd will also P = P_ - ( i + 1 ) 9 give the value of The value of ( 1 − 2μh + ...
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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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