An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 páginas |
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Página 3
... limits the name of Laplace's Coefficients to Zonal Harmonics , and designates all other spherical harmonics by the name of Laplace's Functions . The Zonal Harmonic in the case which we shall consider in the following chapter , i.e. , in ...
... limits the name of Laplace's Coefficients to Zonal Harmonics , and designates all other spherical harmonics by the name of Laplace's Functions . The Zonal Harmonic in the case which we shall consider in the following chapter , i.e. , in ...
Página 17
... T - 2 ) + ( i − m ) ( i + m + 1 ) [ PP „ & u = 0 , - - i άμ άμ since the second term vanishes identically . F. H. 2 2 / - Hence , taking the integral between the limits 1 ZONAL HARMONICS . 17 Expression of any function of μ.
... T - 2 ) + ( i − m ) ( i + m + 1 ) [ PP „ & u = 0 , - - i άμ άμ since the second term vanishes identically . F. H. 2 2 / - Hence , taking the integral between the limits 1 ZONAL HARMONICS . 17 Expression of any function of μ.
Página 18
Norman Macleod Ferrers. - Hence , taking the integral between the limits 1 and +1 , we remark that the factor 1-2 vanishes at both limits , and therefore , except when i - m , or i + m + 1 = 0 , [ P.Pd = 0 . -1 αμ We may remark also that ...
Norman Macleod Ferrers. - Hence , taking the integral between the limits 1 and +1 , we remark that the factor 1-2 vanishes at both limits , and therefore , except when i - m , or i + m + 1 = 0 , [ P.Pd = 0 . -1 αμ We may remark also that ...
Página 25
... limits are equal and opposite . Hence , ( m + i being even ) 1 m 1 [ __ " P ,. dp = 2 [ ' μ " P. dp μη S μm m and then Su " P. du = = 0 , if mi - 2 , i - 4 ...... μ We may proceed to investigate the value of S 1 μm Pi · αμ , if m have ...
... limits are equal and opposite . Hence , ( m + i being even ) 1 m 1 [ __ " P ,. dp = 2 [ ' μ " P. dp μη S μm m and then Su " P. du = = 0 , if mi - 2 , i - 4 ...... μ We may proceed to investigate the value of S 1 μm Pi · αμ , if m have ...
Página 26
... limits -1 and 1 , all the terms on the right - hand side will disappear except C , P , du , which will -1 2 become equal to C1 . 2i + 1 1 2i + 1 Hence 2 -1 m C1 = 2i + 1 f ' μ ~ P , dp , αμ , which is equal to 0 , if m + be odd . Hence ...
... limits -1 and 1 , all the terms on the right - hand side will disappear except C , P , du , which will -1 2 become equal to C1 . 2i + 1 1 2i + 1 Hence 2 -1 m C1 = 2i + 1 f ' μ ~ P , dp , αμ , which is equal to 0 , if m + be odd . Hence ...
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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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