These Matlab functions to compute the phase function for the Bessel and Airy functions and their derivatives. Derivation can be found in:
- Horsley, D.E. Numer. Math. (2017) 136: 679. https://doi.org/10.1007/s00211-016-0853-7
phase = besselphase(nu,x) computes
θν(x) = arctan(Yν(x)/Jν(x))
where Jν and Yν are the Bessel functions of the first and
second kind. The branch is determined by continuity and θν(0) = -π/2
phase = besselprimephase(nu,x) computes
φν(x) = arctan(Y'ν(x)/J'ν(x)) where
J'ν and Y'ν are the derivatives with respect to the
argument of the Bessel functions of the first and second kind. The branch is
determined by continuity and φν(0) = π/2
phase = airyphase(x) computes θ(x) = arctan(A(x)/B(x)) where A and
B are the Airy functions of the first and second kind. The branch is determined
by continuity and θ(0) = π/6
phase = airyprimephase(x) computes φ(x) = arctan(A'(x)/B'(x)) where A' and
B' are the derivatives of the Airy functions of the first and second kind. The
branch is determined by continuity and φ(0) = -π/6