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The differential equation in question is of the second order and has three regular singular points. It is usually denoted by
where a, b, c are the singular points, a, a′ etc. the exponents at those singularities. The solution when no one of the numbers α – α′, β – β′, γ – γ′ is an integer or zero is well known; all types of solution are expressible in terms of the hypergeometric functions.
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* (a) Gesammelte Werke VI, 184–202.
(b) Journal für Math. 56 (1859). 149–165.
* Quart. J. of Math. 39 (1908) 107.
† The notation 
is best reserved for the functions of §4 which, for λ=0, reduce to associated Legendre Functions.
* When λ = 0, these functions become the associated Legendre functions.
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