Heun's Differential Equation

$${d^2w\over dx^2}+\left({{\gamma\over x}+{\delta\over x-1}+{\... ...-a}}\right){dw\over dx}+{\alpha\beta x-q\over x(x-1)(x-a)} w=0$$

where

$$\alpha+\beta-\gamma-\delta-\epsilon+1=0.$$

References

Erdelyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 3. New York: Krieger, pp. 57-62, 1981.

Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, p. 576, 1990.