Please feel free to enjoy my contributions to these interesting fields:

Numerical solution for 3D Poisson equation in circular cylindrical coordinates : Cohl et. al. ( 1997, 1999a)
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)

1997 - Cohl, H. S., Xian-He Sun and J. E. Tohline
"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, 527, 86-101.
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, 321, 5/6, 363-372.
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, 64, 5, 52509.
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

... equation.

This paper, in a modified form, was presented in a poster format at the 200th IAU symposium on binary star formation (held in Potsdam, Germany April 10-15, 2000).

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... Kugelfunctionen,''

Richard Askey, general editor for the section on special functions in the ``Encyclopedia of Mathematics and it's Applications,'' in his forward to Miller (1977) says, in regard to the addition theorem for spherical harmonics and the corresponding addition theorem for trigonometric functions, ``... (these) are among the most important facts known about these functions.'' Whittaker and Watson (1943) further expound on the addition theorems in chapter XV on Legendre functions. Watson (1944) devotes his chapter XI to the discussion of the addition theorems known then for Bessel functions. Hobson (1931) devotes his chapter VIII to the discussion of the addition theorems known then for associated Legendre functions. Hobson (1931) proclaims of Heine's ``Inaugural dissertation...which has hitherto been the only treatise dealing with the functions which could claim to be complete...'' and in connection with Eduard Heine,``...he first introduced the Legendre's functions of the second kind, together with the associated functions.''

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... derive,

Once the main result (16) was derived, the solution's form in terms of toroidal functions suggested that the Green's function in toroidal coordinates should be examined with care. In so doing we have noticed that there is a typographical error in eq. (10.3.81) in Morse & Feshbach's (1953) expression of the Gamma functions in their double summation Green's function expansion in toroidal coordinates (10.3.81). The appearance of integer powers of i in Morse & Feshbach's presentation of the double summation expressions in prolate spheroidal coordinates (10.3.53), oblate spheroidal coordinates (10.3.63), and toroidal coordinates (10.3.81) is not understood. This seemingly inaccurate trait of associated Legendre functions is further demonstrated in their numerical tables VII, VIII, and IX of the associated Legendre functions at the end of Part II of their series. There is also an error in their accounting of Heine's identity, eq. (19), in two separate locations; eq. (10.3.79) and the last equation that appears in their chap. 10. In both locations, the Neumann factor $\epsilon_m = 2 - \delta_{m0},$ is missing. The Neumann factor is a natural consequence of going from a complex exponential notation (Fourier series) to a cosine representation (purely real) of a series. If Morse & Feshbach (1953) had noticed these minor errors in their presentation, the results presented in this paper would most likely have already been completely established.

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