# 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)`

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