This is documentation for an old release of SciPy (version 0.18.1). Read this page in the documentation of the latest stable release (version 1.15.1).
scipy.special.j0¶
- scipy.special.j0(x) = <ufunc 'j0'>¶
Bessel function of the first kind of order 0.
Parameters: x : array_like
Argument (float).
Returns: J : ndarray
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.
Notes
The domain is divided into the intervals [0, 5] and (5, infinity). In the first interval the following rational approximation is used:
J0(x)≈(w−r21)(w−r22)P3(w)Q8(w),where w=x2 and r1, r2 are the zeros of J0, and P3 and Q8 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 [R392] routine j0.
References
[R392] (1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html