ComplexBessel

Complex Bessel Function Numerical Evaluation Note

Optimized Code

DoubleDouble |ν| \leq 256

Im(z) < 0

Complex Bessel functions are analytically connected so that they are complex conjugate symmetrically about the real axis.

DLMF 10.11
DLMF 10.34

Re(z) < 0, Im(z) ≥ 0

Complex Bessel functions are defined to be discontinuous on the negative real axis.

DLMF 10.11
DLMF 10.34

Re(z) ≥ 0, Im(z) ≥ 0, Asymptotic Expansion

DLMF 10.17
DLMF 10.40

Numerical Evaluation Stability

BesselJ, BesselY	BesselI	BesselK

Connection Formula

DLMF 10.27

Reference

DLMF
Wolfram Math World

Author

T.Yoshimura