/NumPy 1.17

numpy.arcsinh

`numpy.arcsinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arcsinh'>`

Inverse hyperbolic sine element-wise.

Parameters: `x : array_like` Input array. `out : ndarray, None, or tuple of ndarray and None, optional` A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or `None`, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. `where : array_like, optional` This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default `out=None`, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. `out : ndarray or scalar` Array of the same shape as `x`. This is a scalar if `x` is a scalar.

Notes

`arcsinh` is a multivalued function: for each `x` there are infinitely many numbers `z` such that `sinh(z) = x`. The convention is to return the `z` whose imaginary part lies in `[-pi/2, pi/2]`.

For real-valued input data types, `arcsinh` always returns real output. For each value that cannot be expressed as a real number or infinity, it returns `nan` and sets the `invalid` floating point error flag.

For complex-valued input, `arccos` is a complex analytical function that has branch cuts `[1j, infj]` and `[-1j, -infj]` and is continuous from the right on the former and from the left on the latter.

The inverse hyperbolic sine is also known as `asinh` or `sinh^-1`.

References

 [1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/
 [2] Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arcsinh

Examples

```>>> np.arcsinh(np.array([np.e, 10.0]))
array([ 1.72538256,  2.99822295])
```