Hypergeometric function

In mathematics, the hypergeometric differential equation is a second-order linear differential equation whose solutions are given by the hypergeometric series. The differential equation is

$z(1-z){\frac {d^{2}w}{dz^{2}}}+\left[c-(a+b+1)z\right]{\frac {dw}{dz}}-abw=0.$

It has three regular singular points 0,1 and $\infty$. When none of the number c, c − a − b or a &minus b are integers, then the equation has two linearly independent solutions.