File Exchange

## specialphase

version 1.0.1.0 (3.5 KB) by David E. Horsley

### David E. Horsley (view profile)

Compute the phase functions of the Bessel functions and their derivative

Updated 29 Jun 2017

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

### Cite As

David E. Horsley (2020). specialphase (https://www.github.com/widdma/specialphase), GitHub. Retrieved .