Arfken (1970) and Morse and Feshbach (1953) use slightly different definitions of these coordinates.
The system used in *Mathematica*
(Wolfram Research, Inc., Champaign, Illinois) is

(1) | |||

(2) | |||

(3) |

where . The Notation of Byerly replaces with , and and with and . The above equations give

(4) |

(5) |

(6) |

(7) | |||

(8) | |||

(9) |

The Laplacian is

(10) |

**References**

Arfken, G. ``Conical Coordinates (, , ).'' §2.16 in
*Mathematical Methods for Physicists, 2nd ed.* Orlando, FL: Academic Press, pp. 118-119, 1970.

Byerly, W. E. *An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics,
with Applications to Problems in Mathematical Physics.* New York: Dover, p. 263, 1959.

Morse, P. M. and Feshbach, H. *Methods of Theoretical Physics, Part I.* New York: McGraw-Hill, p. 659, 1953.

Spence, R. D. ``Angular Momentum in Sphero-Conal Coordinates.'' *Amer. J. Phys.* **27**, 329-335, 1959.

© 1996-9

1999-05-26