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 that ...
... 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 that ...
Seite 2
... obtained from U , by multiplying by 2 + 1 Such an expression as V , we shall call a Solid Spherical Harmonic of the degree . The result obtained by dividing by r , which will be a function of two inde- pendent variables and only , we ...
... obtained from U , by multiplying by 2 + 1 Such an expression as V , we shall call a Solid Spherical Harmonic of the degree . The result obtained by dividing by r , which will be a function of two inde- pendent variables and only , we ...
Seite 6
... obtain , for the most general form of ƒ ( μ ) , αμ ƒ ( μ ) = CP , + C , P. √ p2 ( 1 — μ3 ) - Now , P. being a rational integral function of μ of i dimensions , it may be seen that So αμ ( 1 − μ3 ) P2 - will assume the form of the sum ...
... obtain , for the most general form of ƒ ( μ ) , αμ ƒ ( μ ) = CP , + C , P. √ p2 ( 1 — μ3 ) - Now , P. being a rational integral function of μ of i dimensions , it may be seen that So αμ ( 1 − μ3 ) P2 - will assume the form of the sum ...
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 + α1 ) ( x + α2 ) ... ( x + α ̧ ) ( x + B1 ) ( x + ẞ2 ) ... .. ( 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 + α1 ) ( x + α2 ) ... ( x + α ̧ ) ( x + B1 ) ( x + ẞ2 ) ... .. ( x + B1 ) , i.e. the ...
Seite 16
... . We shall 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 . Proof that.
... . We shall 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 . 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
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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