On Spheroidal Harmonics
1914 ◽
Vol 33
◽
pp. 65-68
Keyword(s):
Ellipsoidal harmonics are defined to be those solutions of Laplace's equation(where x, y, z are rectangular coordinates) which are useful in problems relating to ellipsoids. If the equationrepresents a family of confocal quadrics, it is known that the ellipsoidal harmonics belonging to the family are products of the formwhere l1, l2… are constants: one term is to be picked out of the square brackets as a multiplier of the other factors. Now if we consider the case in which two of the principal axes of the ellipsoids are equal, the latter become spheroids. If then we put b = 0 in (1) the family of confocal spheroids has the equationand belonging to this family there will be spheroidal harmonics of the form given by (2) with b zero.
1914 ◽
Vol 33
◽
pp. 118-121
◽
1916 ◽
Vol 35
◽
pp. 32-37
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Keyword(s):
1944 ◽
Vol 62
(1)
◽
pp. 31-36
1939 ◽
Vol 6
(1)
◽
pp. 24-45
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1963 ◽
Vol 3
(4)
◽
pp. 396-407
◽
Keyword(s):
1925 ◽
Vol 44
◽
pp. 22-25
Keyword(s):
1945 ◽
Vol 7
(2)
◽
pp. 81-82
Keyword(s):
1915 ◽
Vol 34
◽
pp. 102-108
◽
Keyword(s):