Consider the hypergeometric equation (x(1-x) y^{prime prime}+[b-(2+b) x] y^{prime}-b y=0), where (b) is a constant larger than

Question:

Consider the hypergeometric equation $x(1-x) y^{\prime \prime}+[b-(2+b) x] y^{\prime}-b y=0$, where $b$ is a constant larger than unity. Using a Frobenius method, show that the series solution about $x=0$ is the geometric series such that $y_{1}(x)=1+x+x^{2}+\ldots$

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