jv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])
fqe.wavefunction.jv()
jv(v, z)
Bessel function of the first kind of real order and complex argument.
Parameters
v : array_like Order (float). z : array_like Argument (float or complex).
Returns
J : ndarray
Value of the Bessel function, :math:J_v(z).
Notes
For positive v values, the computation is carried out using the AMOS
[1]_ zbesj routine, which exploits the connection to the modified
Bessel function :math:I_v,
.. math:: J_v(z) = \exp(v\pi\imath/2) I_v(-\imath z)\qquad (\Im z > 0)
J_v(z) = \exp(-v\pi\imath/2) I_v(\imath z)\qquad (\Im z < 0)
For negative v values the formula,
.. math:: J_{-v}(z) = J_v(z) \cos(\pi v) - Y_v(z) \sin(\pi v)
is used, where :math:Y_v(z) is the Bessel function of the second
kind, computed using the AMOS routine zbesy. Note that the second
term is exactly zero for integer v; to improve accuracy the second
term is explicitly omitted for v values such that v = floor(v).
Not to be confused with the spherical Bessel functions (see spherical_jn).
See also
jve : :math:J_v with leading exponential behavior stripped off.
spherical_jn : spherical Bessel functions.
References
.. [1] Donald E. Amos, "AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order", http://netlib.org/amos/