An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 páginas |
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Página 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 ) , V1 expressed by where r2 = x2 + y2 + z2 . pli + 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 ) , V1 expressed by where r2 = x2 + y2 + z2 . pli + 1 For the equation ( 1 ) when ...
Página 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 ...
Página 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 ...
Página 17
... positive integers , S ' P.Pdμ = 0 . -1 1 / 2 And Ραμ = 2i +1 • 2 ; +1 The following is a proof of the first property . We have d αμ đμ { ( 1 − μ3 ) - με dPa αμς + i ( i + 1 ) P ; = 0 , d dμ { ( 1 − μ3 ) dP m -- άμ + m ( m + 1 ) Pm = 0 ...
... positive integers , S ' P.Pdμ = 0 . -1 1 / 2 And Ραμ = 2i +1 • 2 ; +1 The following is a proof of the first property . We have d αμ đμ { ( 1 − μ3 ) - με dPa αμς + i ( i + 1 ) P ; = 0 , d dμ { ( 1 − μ3 ) dP m -- άμ + m ( m + 1 ) Pm = 0 ...
Página 18
... positive integers . Hence we need only discuss the case in which m = i . We may remark , however , that since P = P - ( i + 1 ) , of f * P ; du will also the determination of the value of P du will also give the value of The value of ...
... positive integers . Hence we need only discuss the case in which m = i . We may remark , however , that since P = P - ( i + 1 ) , of f * P ; du will also the determination of the value of P du will also give the value of The value of ...
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An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them N M (Norman MacLeod) 1829-19 Ferrers Sin vista previa disponible - 2015 |
Términos y frases comunes
A. S. WALPOLE A. W. VERRALL ALGEBRA ARITHMETIC Assistant Master Assistant-Master axis BEGINNERS BOOK Cambridge centre CHEMISTRY Christ's College Clifton College coefficients cos² Crown 8vo degree denoted density Edited by E. S. Edited by Rev ellipsoid English Exercises expression external point Extra fcap Fcap Fellow of St Fellow of Trinity Globe 8vo GRAMMAR Hence HISTORY internal Introduction and Notes J. P. MAHAFFY John's College late Fellow LATIN Lecturer Litt LL.D Macmillan's Mathematics numerous Illustrations obtain Owens College Oxford P₁ P₂ plane potential preparation PRIMER radius rational integral function revised and enlarged School Second Edition solid solid harmonic sphere spherical harmonic surface harmonic Tesseral Translated Trinity College University V₁ Vocabulary y+b² y+c² zonal harmonic αμ αμσ μ² µ³
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