An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them |
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Page x
... Introduction of Ellipsoidal Harmonics 2. Definition of Elliptic Co - ordinates 3. Transformation of the fundamental equation • 5. Introduction of the quantities E , H 4. Further transformation 6 , 7. Number of values of E of the degree ...
... Introduction of Ellipsoidal Harmonics 2. Definition of Elliptic Co - ordinates 3. Transformation of the fundamental equation • 5. Introduction of the quantities E , H 4. Further transformation 6 , 7. Number of values of E of the degree ...
Page 13
... introducing an im- portant theorem , due to Rodrigues , properly belonging to the Differential Calculus , but which is of great use in this subject . The theorem in question is as follows : If m be any integer less than i , ... di - m ...
... introducing an im- portant theorem , due to Rodrigues , properly belonging to the Differential Calculus , but which is of great use in this subject . The theorem in question is as follows : If m be any integer less than i , ... di - m ...
Page 16
... Introducing the condition that P , is that value of ƒ ( u ) . which is equal to 1 , when μ = 1 , we get Pi = 1 d ' 2o.1.2 ... i dμ3 ( μ2 — 1 ) ' . 10. We shall now establish two very important proper- ties of the function P ; and apply ...
... Introducing the condition that P , is that value of ƒ ( u ) . which is equal to 1 , when μ = 1 , we get Pi = 1 d ' 2o.1.2 ... i dμ3 ( μ2 — 1 ) ' . 10. We shall now establish two very important proper- ties of the function P ; and apply ...
Page 47
... introduction of the expressions for zonal har- monics in the form of definite integrals , it will be found that if the value of either of these potentials for any point in the axis be denoted by ( z ) , the corresponding value for any ...
... introduction of the expressions for zonal har- monics in the form of definite integrals , it will be found that if the value of either of these potentials for any point in the axis be denoted by ( z ) , the corresponding value for any ...
Page 104
... ( v ) P2 ( μ ) + · 1 ... more 3. The expression for Q , may be thrown into a convenient form , by introducing into the numerator and de- nominator of the coefficient of each term , the factor 104 SPHERICAL HARMONICS OF THE SECOND KIND .
... ( v ) P2 ( μ ) + · 1 ... more 3. The expression for Q , may be thrown into a convenient form , by introducing into the numerator and de- nominator of the coefficient of each term , the factor 104 SPHERICAL HARMONICS OF THE SECOND KIND .
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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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