scipy.special.itairy — SciPy v1.15.3 Manual (original) (raw)

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

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()