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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)(z>0)Jv(z)=exp(nπı/2)Iv(ız)(z<0)

For negative v values the formula,

Jv(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/

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