DOC: add Examples and fix docstring for special.airye

[AtsushiSakai]

Reference issue

fix a part of #7168

What does this implement/fix?

add Examples and fix docstring for special.airye()

[ilayn]

You might want to use the OOP style as matplotlib fols recommend its usage

from scipy.special import airye
import matplotlib.pyplot as plt
z = np.linspace(40, 200)
eAi, eAip, eBi, eBip = airye(x)
f, ax = plt.subplots(2, 1, sharex=True)
for ind, data in enumerate([[eAi, eBi, ["eAi", "eBi"]],
                            [eAip, eBip, ["eAip", "eBip"]]]):
    ax[ind].plot(z, data[0], "-r", z, data[1], "-b")
    ax[ind].legend(data[2])
    ax[ind].grid()

[person142]

The interesting thing about these functions is the “exponentially scaled” bit, so for an example I would want to see something that compares them to the normal Airy functions so that you can see what they are exponentially scaled compared to.

[pv]

And maybe some example where the usual non-scaled functions under/overflow whereas the exponentially scaled ones do not, so that the reason for the existence of these functions becomes clearer.

[AtsushiSakai]

Thank you guys for reviewing and comments. I updated it based on your feedbacks. PTAL.

[AtsushiSakai]

Close and reopen to rerun CI

[ilayn]

This is quite nice now. Thanks @AtsushiSakai @pv