An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 sider |
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Resultat 1-5 av 24
Side 7
... denote by P ,, or P. ( u ) , that particular form of the integral which assumes the value unity when μ is put equal to unity . We shall next prove the following important proposition . If h be less than unity , and if ( 1 – 2μh + h ) ...
... denote by P ,, or P. ( u ) , that particular form of the integral which assumes the value unity when μ is put equal to unity . We shall next prove the following important proposition . If h be less than unity , and if ( 1 – 2μh + h ) ...
Side 10
... denoted by P. We have thus 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 ...
... denoted by P. We have thus 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 ...
Side 12
... denote a quantity , such that h being less than 1 . Then Also dy dμ = y - 1 1 h - 1 2μ + h h2 - 2 = = 1 2μ 11 + h h2 1 ( 1 − 2μh + h2 ) 3 * 2μ h 1 + h2 2y 2μ ..y - 3-1-3 ; :: y2 = 1 h - h y = μ + h ( V2 = 1 ) . Hence , by Lagrange's ...
... denote a quantity , such that h being less than 1 . Then Also dy dμ = y - 1 1 h - 1 2μ + h h2 - 2 = = 1 2μ 11 + h h2 1 ( 1 − 2μh + h2 ) 3 * 2μ h 1 + h2 2y 2μ ..y - 3-1-3 ; :: y2 = 1 h - h y = μ + h ( V2 = 1 ) . Hence , by Lagrange's ...
Side 20
... denoting the values which P. , respectively assume , when -μ is written for u . PP or -P , according as i is P involves only odd , or only even , as i is odd or even * . Assume then even or odd . 1 P , ... P1 , Hence That is , powers of ...
... denoting the values which P. , respectively assume , when -μ is written for u . PP or -P , according as i is P involves only odd , or only even , as i is odd or even * . Assume then even or odd . 1 P , ... P1 , Hence That is , powers of ...
Side 39
... denoted by a and b in this equation is that b2 should not be greater than a2 . For , if b2 be not greater than a2 , cos I cannot become equal to while increases from 0 to π , and therefore the Ђ expression under the integral sign cannot ...
... denoted by a and b in this equation is that b2 should not be greater than a2 . For , if b2 be not greater than a2 , cos I cannot become equal to while increases from 0 to π , and therefore the Ђ expression under the integral sign cannot ...
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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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