# Question:Expansions for hypergeom

## Question:Expansions for hypergeom

It would be nice to have asymptotics for hypergeom that are valid around abs(z)=infinity for any value of argument(z):

```limit(hypergeom([1, 1], [2, 2], I*z), z = infinity); # zero
limit(hypergeom([1, 1], [2, 2], I z), z = infinity)
```

series and asympt can give the expansions for +infinity or -infinity, not necessarily valid for other directions. FunctionAdvisor gives only the expansion at +infinity (which in this case is valid for Re(z)>0). Changes of variables like z->-z or z->1/z seem to never work in FunctionAdvisor(asymptotic_expansion, ...).

Also the expansions around z=1:

```limit(hypergeom([1, 1, 1], [1/2, 2], z)*(z-1), z = 1); # zero
/         /           [1   ]   \               \
limit|hypergeom|[1, 1, 1], [-, 2], z| (z - 1), z = 1|
\         \           [2   ]   /               /
```

And on the branch cuts:

```limit(hypergeom([1/3, 1/3], [1/2], 2+I*a), a = 0); # the directional limits are different
/[1  1]  [1]   \
hypergeom|[-, -], [-], 2|
\[3  3]  [2]   /
```

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