Read More
Date: 24-5-2018
900
Date: 11-6-2018
824
Date: 13-6-2018
740
|
The ordinary differential equation
(1) |
(Byerly 1959, p. 255). The solution is denoted and is known as an ellipsoidal harmonic of the first kind, or Lamé function. Whittaker and Watson (1990, pp. 554-555) give the alternative forms
(2) |
|
(3) |
|
(4) |
|
(5) |
|
(6) |
(Whittaker and Watson 1990, pp. 554-555; Ward 1987; Zwillinger 1997, p. 124). Here, is a Weierstrass elliptic function, is a Jacobi elliptic function, and
(7) |
|||
(8) |
|||
(9) |
Two other equations named after Lamé are given by
(10) |
and
(11) |
(Moon and Spencer 1961, p. 157; Zwillinger 1997, p. 124).
REFERENCES:
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, 1959.
Moon, P. and Spencer, D. E. Field Theory for Engineers. New York: Van Nostrand, 1961.
Ward, R. S. "The Nahm Equations, Finite-Gap Potentials and Lamé Functions." J. Phys. A: Math. Gen. 20, 2679-2683, 1987.
Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 1990.
Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 124, 1997.
|
|
علامات بسيطة في جسدك قد تنذر بمرض "قاتل"
|
|
|
|
|
أول صور ثلاثية الأبعاد للغدة الزعترية البشرية
|
|
|
|
|
مستشفى العتبة العباسية الميداني في سوريا يقدّم خدماته لنحو 1500 نازح لبناني يوميًا
|
|
|