An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them |
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Page 10
... greater than 1 , this series becomes divergent . But we may write ( h2 — 2μh + 1 ) −1 = } = 1 ( Po + f ++ .. + fit ... ) , ( 1-2 + μ 1 h h2 P2 + 1 since is less than 1 , h P P P hi = + + + + ..... h h2 ... Hence P is also the ...
... greater than 1 , this series becomes divergent . But we may write ( h2 — 2μh + 1 ) −1 = } = 1 ( Po + f ++ .. + fit ... ) , ( 1-2 + μ 1 h h2 P2 + 1 since is less than 1 , h P P P hi = + + + + ..... h h2 ... Hence P is also the ...
Page 32
... expressions i may be any integer such that mi is even , i being not greater than m . Hence they will always be negative , except when i is equal to m . 20. We may apply these expressions to develop cos me 32 ZONAL HARMONICS .
... expressions i may be any integer such that mi is even , i being not greater than m . Hence they will always be negative , except when i is equal to m . 20. We may apply these expressions to develop cos me 32 ZONAL HARMONICS .
Page 39
... 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 become infinite . Supposing then that we write z for a , and ...
... 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 become infinite . Supposing then that we write z for a , and ...
Page 44
... the attracted point lie within the sphere of which the ring is a great circle , and the series ( 2 ) if z be greater than c , or if the attracted point lie without this sphere . Now , take any point whose distance from the centre.
... the attracted point lie within the sphere of which the ring is a great circle , and the series ( 2 ) if z be greater than c , or if the attracted point lie without this sphere . Now , take any point whose distance from the centre.
Page 45
... greater than c , while ( 1 ' ) becomes equal to ( 2 ' ) when r = c , and will therefore denote the required potential for all values of r less than c . These expressions may be reduced to other forms by means of the expressions ...
... greater than c , while ( 1 ' ) becomes equal to ( 2 ' ) when r = c , and will therefore denote the required potential for all values of r less than c . These expressions may be reduced to other forms by means of the expressions ...
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Common terms and phrases
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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