scipy.special.itairy#
- scipy.special.itairy(x, out=None) = <ufunc 'itairy'>#
Integrals of Airy functions
Calculates the integrals of Airy functions from 0 to x.
- Parameters:
- xarray_like
Upper limit of integration (float).
- outtuple of ndarray, optional
Optional output arrays for the function values
- Returns:
- Aptscalar or ndarray
Integral of Ai(t) from 0 to x.
- Bptscalar or ndarray
Integral of Bi(t) from 0 to x.
- Antscalar or ndarray
Integral of Ai(-t) from 0 to x.
- Bntscalar or ndarray
Integral of Bi(-t) from 0 to x.
Notes
Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin [1].
References
[1]Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f_src/special_functions/special_functions.html
Examples
Compute the functions at
x=1.
.>>> import numpy as np >>> from scipy.special import itairy >>> import matplotlib.pyplot as plt >>> apt, bpt, ant, bnt = itairy(1.) >>> apt, bpt, ant, bnt (0.23631734191710949, 0.8727691167380077, 0.46567398346706845, 0.3730050096342943)
Compute the functions at several points by providing a NumPy array for x.
>>> x = np.array([1., 1.5, 2.5, 5]) >>> apt, bpt, ant, bnt = itairy(x) >>> apt, bpt, ant, bnt (array([0.23631734, 0.28678675, 0.324638 , 0.33328759]), array([ 0.87276912, 1.62470809, 5.20906691, 321.47831857]), array([0.46567398, 0.72232876, 0.93187776, 0.7178822 ]), array([ 0.37300501, 0.35038814, -0.02812939, 0.15873094]))
Plot the functions from -10 to 10.
>>> x = np.linspace(-10, 10, 500) >>> apt, bpt, ant, bnt = itairy(x) >>> fig, ax = plt.subplots(figsize=(6, 5)) >>> ax.plot(x, apt, label=r"$\int_0^x\, Ai(t)\, dt$") >>> ax.plot(x, bpt, ls="dashed", label=r"$\int_0^x\, Bi(t)\, dt$") >>> ax.plot(x, ant, ls="dashdot", label=r"$\int_0^x\, Ai(-t)\, dt$") >>> ax.plot(x, bnt, ls="dotted", label=r"$\int_0^x\, Bi(-t)\, dt$") >>> ax.set_ylim(-2, 1.5) >>> ax.legend(loc="lower right") >>> plt.show()