scipy.special.j0¶

scipy.special.
j0
(x) = <ufunc 'j0'>¶ Bessel function of the first kind of order 0.
 Parameters
 xarray_like
Argument (float).
 Returns
 Jndarray
Value of the Bessel function of the first kind of order 0 at x.
See also
jv
Bessel function of real order and complex argument.
spherical_jn
spherical Bessel functions.
Notes
The domain is divided into the intervals [0, 5] and (5, infinity). In the first interval the following rational approximation is used:
\[J_0(x) \approx (w  r_1^2)(w  r_2^2) \frac{P_3(w)}{Q_8(w)},\]where \(w = x^2\) and \(r_1\), \(r_2\) are the zeros of \(J_0\), and \(P_3\) and \(Q_8\) are polynomials of degrees 3 and 8, respectively.
In the second interval, the Hankel asymptotic expansion is employed with two rational functions of degree 6/6 and 7/7.
This function is a wrapper for the Cephes [1] routine
j0
. It should not be confused with the spherical Bessel functions (seespherical_jn
).References
 1
Cephes Mathematical Functions Library, http://www.netlib.org/cephes/