scipy.special.hyp1f1¶
- scipy.special.hyp1f1(a, b, x, out=None) = <ufunc 'hyp1f1'>¶
Confluent hypergeometric function 1F1.
The confluent hypergeometric function is defined by the series
\[{}_1F_1(a; b; x) = \sum_{k = 0}^\infty \frac{(a)_k}{(b)_k k!} x^k.\]See [dlmf] for more details. Here \((\cdot)_k\) is the Pochhammer symbol; see
poch.- Parameters
- a, barray_like
Real parameters
- xarray_like
Real or complex argument
- outndarray, optional
Optional output array for the function results
- Returns
- scalar or ndarray
Values of the confluent hypergeometric function
See also
References
- dlmf
NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/13.2#E2
Examples
>>> import scipy.special as sc
It is one when x is zero:
>>> sc.hyp1f1(0.5, 0.5, 0) 1.0
It is singular when b is a nonpositive integer.
>>> sc.hyp1f1(0.5, -1, 0) inf
It is a polynomial when a is a nonpositive integer.
>>> a, b, x = -1, 0.5, np.array([1.0, 2.0, 3.0, 4.0]) >>> sc.hyp1f1(a, b, x) array([-1., -3., -5., -7.]) >>> 1 + (a / b) * x array([-1., -3., -5., -7.])
It reduces to the exponential function when a = b.
>>> sc.hyp1f1(2, 2, [1, 2, 3, 4]) array([ 2.71828183, 7.3890561 , 20.08553692, 54.59815003]) >>> np.exp([1, 2, 3, 4]) array([ 2.71828183, 7.3890561 , 20.08553692, 54.59815003])