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scipy.special.jn¶
- scipy.special.jn(v, z) = <ufunc 'jv'>¶
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, Jv(z).
See also
- jve
- Jv with leading exponential behavior stripped off.
Notes
For positive v values, the computation is carried out using the AMOS [R394] zbesj routine, which exploits the connection to the modified Bessel function Iv,
Jv(z)=exp(nπı/2)Iv(−ız)(ℑz>0)Jv(z)=exp(−nπı/2)Iv(ız)(ℑz<0)For negative v values the formula,
J−v(z)=Jv(z)cos(πv)−Yv(z)sin(πv)is used, where Yv(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
[R394] (1, 2) Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/