scipy.special.spherical_jn¶
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scipy.special.spherical_jn(n, z, derivative=False)[source]¶ Spherical Bessel function of the first kind or its derivative.
Defined as [1],
\[j_n(z) = \sqrt{\frac{\pi}{2z}} J_{n + 1/2}(z),\]where \(J_n\) is the Bessel function of the first kind.
- Parameters
- nint, array_like
Order of the Bessel function (n >= 0).
- zcomplex or float, array_like
Argument of the Bessel function.
- derivativebool, optional
If True, the value of the derivative (rather than the function itself) is returned.
- Returns
- jnndarray
Notes
For real arguments greater than the order, the function is computed using the ascending recurrence [2]. For small real or complex arguments, the definitional relation to the cylindrical Bessel function of the first kind is used.
The derivative is computed using the relations [3],
\[ \begin{align}\begin{aligned}j_n'(z) = j_{n-1}(z) - \frac{n + 1}{z} j_n(z).\\j_0'(z) = -j_1(z)\end{aligned}\end{align} \]New in version 0.18.0.
References