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for some calculation I need the behaviour of the hypergeometric function 2F1 near [tex]z=\tfrac{1}{2}[/tex]. Specifically I need

[tex]_2 F_1(\mu,1-\mu,k,\tfrac{1}{2}+i x)[/tex]

with [tex] x\in \mathbb{R} [/tex] near 0, and [tex]1/2\leq\mu\leq 2[/tex], [tex]1\leq k \in \mathbb{N}[/tex].

Differentiating around x=0 and writing the Taylor series gives a result, although very nasty and not really useful.

Does anybody know of an expansion around this point?

Thanks for your help.

betel

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# Hypergeometric Function around z=1/2

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