# tfp.math.hypergeometric.hyp2f1_small_argument

Compute the Hypergeometric function 2f1(a, b, c, z) when |z| <= 1.

Given `a, b, c` and `z`, compute Gauss' Hypergeometric Function, specified by the series:

```1 + (a * b/c) * z + (a * (a + 1) * b * (b + 1) / ((c * (c + 1)) * z**2 / 2 + ... (a)_n * (b)_n / (c)_n * z ** n / n! + ....```

`a` Floating-point `Tensor`, broadcastable with `b, c, z`. Parameter for the numerator of the series fraction.
`b` Floating-point `Tensor`, broadcastable with `a, c, z`. Parameter for the numerator of the series fraction.
`c` Floating-point `Tensor`, broadcastable with `a, b, z`. Parameter for the denominator of the series fraction.
`z` Floating-point `Tensor`, broadcastable `a, b, c`. Value to compute `2F1(a, b, c, z)` at. Only values of `|z| < 1` are allowed.
`name` A name for the operation (optional). Default value: `None` (i.e., 'continued_fraction').

`hypergeo` `2F1(a, b, c, z)`

#### References

[1] F. Johansson. Computing hypergeometric functions rigorously. ACM Transactions on Mathematical Software, August 2019. https://arxiv.org/abs/1606.06977 [2] J. Pearson, S. Olver, M. Porter. Numerical methods for the computation of the confluent and Gauss hypergeometric functions. Numerical Algorithms, August 2016. [3] M. Abramowitz, I. Stegun. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables.

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