scipy.special.jve¶
- scipy.special.jve(v, z) = <ufunc 'jve'>¶
Exponentially scaled Bessel function of order v.
Defined as:
jve(v, z) = jv(v, z) * exp(-abs(z.imag))
Parameters: v : array_like
Order (float).
z : array_like
Argument (float or complex).
Returns: J : ndarray
Value of the exponentially scaled Bessel function.
Notes
For positive v values, the computation is carried out using the AMOS [R400] zbesj routine, which exploits the connection to the modified Bessel function \(I_v\),
\[\begin{split}J_v(z) = \exp(n\pi\imath/2) I_v(-\imath z)\qquad (\Im z > 0)\end{split}\]\[\begin{split}J_v(z) = \exp(-n\pi\imath/2) I_v(\imath z)\qquad (\Im z < 0)\end{split}\]For negative v values the formula,
\[J_{-v}(z) = J_v(z) \cos(\pi v) - Y_v(z) \sin(\pi v)\]is used, where \(Y_v(z)\) 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).
References
[R400] (1, 2) Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/