Definition
The differential equation is given by
![\frac{d^2w}{dz^2} + \left[
\frac{1-\alpha-\alpha'}{z-a} +
\frac{1-\beta-\beta'}{z-b} +
\frac{1-\gamma-\gamma'}{z-c} \right] \frac{dw}{dz}](http://upload.wikimedia.org/math/9/8/9/98909a4101fc979c3ca83fb5f72b5b9f.png)
![+\left[
\frac{\alpha\alpha' (a-b)(a-c)} {z-a}
+\frac{\beta\beta' (b-c)(b-a)} {z-b}
+\frac{\gamma\gamma' (c-a)(c-b)} {z-c}
\right]
\frac{w}{(z-a)(z-b)(z-c)}=0.](http://upload.wikimedia.org/math/b/4/9/b4945a13dcd293dc64b94cfb906dd3e5.png)
The regular singular points are a, b, and c. The pairs of exponents for each are respectively α; α', β;β', and γ;γ'. The exponents are subject to the condition
Read more about this topic: Riemann's Differential Equation
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