An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them |
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Page 3
... consider in the following chapter , i.e. , in which the system is symmetrical about the line from which is measured , was really , however , first introduced by Legendre , although the properties of spherical harmonics in general were ...
... consider in the following chapter , i.e. , in which the system is symmetrical about the line from which is measured , was really , however , first introduced by Legendre , although the properties of spherical harmonics in general were ...
Page 14
... consider the expression ( x + α ̧ ) ( x + α2 ) ... ( x + α1 ) ( x + B1 ) ( x + B2 ) ( x + B1 ) . ... Conceive this differentiated ( I ) im times , ( II ) + m times . The two expressions thus obtained will consist of an equal number of ...
... consider the expression ( x + α ̧ ) ( x + α2 ) ... ( x + α1 ) ( x + B1 ) ( x + B2 ) ( x + B1 ) . ... Conceive this differentiated ( I ) im times , ( II ) + m times . The two expressions thus obtained will consist of an equal number of ...
Page 15
... considering . There remain therefore 2m factors to be accounted for . None of the letters a ' , a " ... a13 ) , B , B ... B Βια B ' , B " ... B , a , a ,, ... α ( g ) can appear there . Hence the remaining factor must involve ma's and m ...
... considering . There remain therefore 2m factors to be accounted for . None of the letters a ' , a " ... a13 ) , B , B ... B Βια B ' , B " ... B , a , a ,, ... α ( g ) can appear there . Hence the remaining factor must involve ma's and m ...
Page 18
... consider the cases in which i - m , or i + m + 1 = 0 . We see that i + m + 1 cannot be equal to 0 , if i and m are both positive integers . Hence we need only discuss the case in which m = i . We may remark , however , that since P1 ...
... consider the cases in which i - m , or i + m + 1 = 0 . We see that i + m + 1 cannot be equal to 0 , if i and m are both positive integers . Hence we need only discuss the case in which m = i . We may remark , however , that since P1 ...
Page 20
... considering a particular example . di dui ( u2 - 1 ) ' . * This is also evident , from the fact that P ; is a constant multiple of Suppose then that we have XC У 2 + + 20 ZONAL HARMONICS . Expression of cos me in a series of zonal ...
... considering a particular example . di dui ( u2 - 1 ) ' . * This is also evident , from the fact that P ; is a constant multiple of Suppose then that we have XC У 2 + + 20 ZONAL HARMONICS . Expression of cos me in a series of zonal ...
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A. S. WALPOLE A. W. VERRALL Assistant Master Assistant-Master axis BEGINNERS BOOK Cambridge centre Classical Clifton College coefficients cos² Crown 8vo degree denoted density Edited by E. S. Edited by Rev ELEMENTARY English Exercises expression external point Extra fcap Fcap Fellow of St Fellow of Trinity Globe 8vo GRAMMAR Hence Illustrations internal Introduction and Notes J. P. MAHAFFY JOHN BOND John's College late Fellow LATIN Lecturer Litt LL.D numerous obtain Owens College Oxford P₁ P₂ plane potential preparation PRIMER radius rational integral function revised and enlarged satisfies the equation School Second Edition sin² solid solid harmonic sphere spherical harmonic suppose surface harmonic Tesseral Translated TREATISE Trinity College University V₁ Vocabulary y+b² y+c² zonal harmonics αμ αμσ µ² µ³
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