# scipy.special.j0¶

scipy.special.j0(x) = <ufunc 'j0'>

Bessel function of the first kind of order 0.

Parameters: x : array_like Argument (float). J : ndarray Value of the Bessel function of the first kind of order 0 at x.

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 [R511] routine j0. It should not to be confused with the spherical Bessel functions (see spherical_jn).

References

 [R511] (1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

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