specialphase

Compute the phase functions of the Bessel functions and their derivative

These Matlab functions to compute the phase function for the Bessel and Airy
functions and their derivatives.
`phase = besselphase(nu,x)` computes θₙ(x) = arctan(Yₙ(x)/Jₙ(x)) where
Jₙ and Yₙ are the Bessel functions of the first and second kind. The
branch is determined by continuity and θₙ(0) = -π/2

`phase = besselprimephase(nu,x)` computes φₙ(x) = arctan(Y'ₙ(x)/J'ₙ(x)) where
J'ₙ and Y'ₙ are the derivatives with respect to theargument of the Bessel
functions of the first and second kind. The branch is determined by continuity
and φₙ(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