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
Famous quotes containing the word definition:
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)