[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
## Generalized Prolate Spheroids

**From**: |
Carl Scarrott |

**Subject**: |
Generalized Prolate Spheroids |

**Date**: |
Tue, 12 Dec 2000 09:18:52 +0000 |

Has anyone developed code for calculating the Generalized Prolate
Spheroidal functions?
They are found from the eigensolution of the integral equation:
lambda*phi(x)=Üint^{1}_{0} J_N(c*x*y) * sqrt(c*x*y) * phi(y) dy
for N=0,1,2,.... where J_N is the Bessel J function of order N, phi(x)
is the eigenfunction and lambda is the corresponding eigenvalue.
They are also the solution of the differential equation:
d/dx{ (1-x^2) * d/dx{phi(x)} } + (chi - (c*x)^2 + (0.25-N^2)/(x^2)) *
phi(x) = 0
where chi is the corresponding eigenvalue.
See Slepian (1964) Bell Sys. Tech. J. 44.
--
Carl Scarrott, BSc, GIMA web : http://www.maths.lancs.ac.uk/þscarrott
Maths & Stats Dept, email : address@hidden
Lancaster University Tel : +44 (0)1524 594145
Lancaster, LA1 4YF, UK. Fax : +44 (0)1524 592681
-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.
Octave's home on the web: http://www.octave.org
How to fund new projects: http://www.octave.org/funding.html
Subscription information: http://www.octave.org/archive.html
-------------------------------------------------------------

**Generalized Prolate Spheroids**,
*Carl Scarrott* **<=**