scipy.special.hyperu#
- scipy.special.hyperu(a, b, x, out=None) = <ufunc 'hyperu'>#
- Confluent hypergeometric function U - It is defined as the solution to the equation \[x \frac{d^2w}{dx^2} + (b - x) \frac{dw}{dx} - aw = 0\]- which satisfies the property \[U(a, b, x) \sim x^{-a}\]- as \(x \to \infty\). See [dlmf] for more details. - Parameters:
- a, barray_like
- Real-valued parameters 
- xarray_like
- Real-valued argument 
- outndarray, optional
- Optional output array for the function values 
 
- Returns:
- scalar or ndarray
- Values of U 
 
 - References [dlmf]- NIST Digital Library of Mathematics Functions https://dlmf.nist.gov/13.2#E6 - Examples - >>> import numpy as np >>> import scipy.special as sc - It has a branch cut along the negative x axis. - >>> x = np.linspace(-0.1, -10, 5) >>> sc.hyperu(1, 1, x) array([nan, nan, nan, nan, nan]) - It approaches zero as x goes to infinity. - >>> x = np.array([1, 10, 100]) >>> sc.hyperu(1, 1, x) array([0.59634736, 0.09156333, 0.00990194]) - It satisfies Kummer’s transformation. - >>> a, b, x = 2, 1, 1 >>> sc.hyperu(a, b, x) 0.1926947246463881 >>> x**(1 - b) * sc.hyperu(a - b + 1, 2 - b, x) 0.1926947246463881