Green's function for 3D Laplace equation : Cohl et. al. ( 1999a, 1999b, 2000, 2001, 2002)

Gravitational potential : Cohl et. al. ( 1999a, 1999b, 2000, 2001, 2002)

Quadrics & cyclides : Cohl et. al. ( 1999a, 1999b, 2000, 2001, 2002)

Heine identity : Cohl et. al. ( 1999a, 1999b, 2000, 2001, 2002)

Cylindrical, toroidal, oblate and prolate spheroidal, parabolic, bispherical coordinate systems : Cohl et. al. (1999a, 2000)

New addition theorems for rotationally invariant coordinate systems which R-separate 3D Laplace equation: Cohl et. al. (1999a, 2000)

3D biharmonic, 3D triharmonic, and 3D higher harmonic Green's functions : Cohl (2002)

Spherical coordinate system : Cohl et. al. (2001)

Coulomb direct (classical) and exchange (quantum) integrals/interactions : Cohl et. al. (2001)

Two-electron interactions : Cohl et. al. (2001)

Spherical azimuthal and separation angle Fourier expansions : Cohl et. al. (2001)

Magnetic field of an infinitesimally thin circular current loop : Cohl & Tohline (1999)

Symmetry properties of associated Legendre/toroidal functions : Cohl et. al. (2000)

Whipple formulae for toroidal/associated Legendre functions : Cohl et. al. (2000)

New addition theorem for spherical coordinates : Cohl et. al. (2001)

Solar White Light Flares : Neidig et. al. (1993)

"Parallel Implementation of a Data-Transpose Technique for the Solution of Poisson's Equation in Cylindrical Coordinates"

Proceedings of the 8th SIAM Conference on Parallel Processing for Scientific Computing, Minneapolis, Minnesota, March.

1999a - Cohl, H. S.

"On the numerical solution of the cylindrical Poisson equation for isolated self-gravitating systems"

The Louisiana State University and Agricultural and Mechanical College, 122 pages

1999b - Cohl, H. S. and J. E. Tohline

"A Compact Cylindrical Green's Function Expansion for the Solution of Potential Problems"

The Astrophysical Journal,

2000 - Cohl, H. S., J. E. Tohline, A. R. P. Rau, H. M. Srivastava

"Developments in determining the gravitational potential using toroidal functions"

Astronomische Nachrichten,

2001 - Cohl, H. S., Rau, A. R. P., Tohline, J. E., Browne, D. A., Cazes, J. E. and Barnes, E. I.

"Useful alternative to the multipole expansion of 1/r potentials"

Physical Review A: Atomic and Molecular Physics and Dynamics,

2002 - Cohl, H. S.

"Portent of Heine's Reciprocal Square Root Identity"

Proceedings of the 3D Stellar Evolution Workshop, ed. R. Cavallo, S. Keller, S. Turcotte, Livermore, California

(40) |

Consequently, the following two expressions must be valid
*definite integrals*:

(41) |

and

(42) |

(43) |

and,

Cohl, H. S., J. E. Tohline, A. R. P. Rau, H. M. Srivastava (2000)