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

Bibliography

Abramowitz & Stegun

CLICK TEXT TO READ PDF COPY OF PAPER

Abramowitz, M. & Stegun, I. A.: 1965, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (New York: Dover)

1

Bateman, H.: 1959, Partial Differential Equations of Mathematical Physics (Cambridge University Press, New York)

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Binney, J., & Tremaine, S.: 1987, Galactic Dynamics (Princeton: Princeton Univ. Press)

Bôcher

Bôcher, M.: 1894, Die Reihenentwickelungen der Potentialtheorie (Leipzig)

3

Cohl, H. S. & Tohline, J. E.: 1999, 527, 86

4

Cohl, H. S., Rau, A. R. P., Tohline, J. E., Browne, D. A., Cazes, J. E., & Barnes, E.: 2000, ``Alternative Expansions for Inverse Square Law Forces,'' in preparation

5

Erdélyi, A., Magnus, W., Oberhettinger, F., & Tricomi, F. G.: 1953, Higher Transcendental Functions, vol. 1 (New York: McGraw-Hill Book Company, Inc.)

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Gradshteyn, I. S. & Ryzhik, I. M.: 1994, Table of Integrals, Series, and Products (New York: Academic Press)

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Heine, E.: 1881, Handbuch der Kugelfunctionen, Theorie und Anwendungen (Physica-Verlag, Wuerzburg, 1961)

8

Hobson, E. W.: 1934, The Theory of Spherical and Ellipsoidal Harmonics (Cambridge: Cambridge University Press)

9

Jackson, J. D.: 1975, Classical Electrodynamics (New York: John Wiley & Sons)

10

Magnus, W., Oberhettinger, F., & Soni R. P.: 1966, Formulas and Theorems for the Special Functions of Mathematical Physics (New York: Springer-Verlag)

11

Miller, W., Jr.: 1968, Lie Theory and Special Functions (New York: Academic Press)

12

------ : 1972, Symmetry Groups and Their Applications (New York: Academic Press)

13

------ : 1977, Symmetry and Separation of Variables (London: Addison-Wesley Publishing Company)

14

Moon, P., & Spencer D. E.: 1961a, Field Theory for Engineers (D. Van Nostrand Company: Princeton)

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Moon, P., & Spencer D. E.: 1961b, Field Theory Handbook: Including Coordinate Systems, Differential Equations and Their Solutions, (Springer-Verlag: Berlin)

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Morse, P., & Feshbach, H.: 1953, Methods of Theoretical Physics (New York: McGraw-Hill Book Company)

17

Watson, G. N.: 1944, A Treatise on the Theory of Bessel Functions (Cambridge: Cambridge Univ. Press)

18

Whittaker, E. T. & Watson, G. N.: 1943, A Course of Modern Analysis (Cambridge: Cambridge Univ. Press)

Howard S. Cohl, Programming Environment & Training, Naval Oceanographic Office Major Shared Resource Center, Stennis Space Center, MS, 39529, U.S.A., e-mail: hcohl@navo.hpc.mil Joel E. Tohline, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, 70803-4001, U.S.A., e-mail: tohline@physics.lsu.edu A.R.P. Rau, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, 70803-4001, U.S.A., e-mail: arau@physics.lsu.edu Hari M. Srivastava, Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3P4, CANADA, e-mail: hmsri@uvvm.uvic.ca

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

Astronomische Nachrichten, 321, 5/6, 363-372.

"Developments in determining the gravitational potential using toroidal functions."

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