An elementary treatise on Laplace's functions, Lame's functions, and Bessel's functions: I. Todhunter

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From the Introduction:
The mathematical expressions to which the present volume is mainly devoted were first introduced by Legendre in some researches relating to the Figure of the Earth, and were much cultivated by himself and by Laplace in their investigations of this important problem of Physical Astronomy. In the History of the Mathematical Theories of Attraction and of the Figure of the Earth will be found an account of the origin and early progress of the branch of analysis which we are now about to expound.

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