The hypergeometric series F(α, β, γ; z) was defined in Exercise 16 of Chapter 1. Show that
Show as a result that the hypergeometric function, initially defined by a power series convergent in the unit disc, can be continued analytically to the complex plane slit along the half-line [1, ∞).
Note that
[Hint: To prove the integral identity, expand (1 − zt) −α as a power series.]
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