Using Darling’s theorem on products of generalized hypergeometric series, an analytic expression is obtained for the Coulomb matrix elements in the lowest Landau level in the representation of angular momentum. The result is important in the studies of fractional quantum Hall effect (FQHE) in disk geometry. Matrix elements are expressed as simple finite sums of positive terms, eliminating the need to approximate these quantities with slowly convergent series. As a by-product, an analytic representation for certain integrals of products of Laguerre polynomials is obtained.
REFERENCES
1.
V. J.
Goldman
and E. V.
Tsiper
, Phys. Rev. Lett.
86
, 5841
(2001
).2.
3.
4.
5.
A.
Cappelli
, C.
Mendez
, J.
Simonin
, and G. R.
Zemba
, Phys. Rev. B
58
, 16291
(1998
).6.
7.
8.
M.
Stone
, H. W.
Wyld
, and R. L.
Schult
, Phys. Rev. B
45
, 14156
(1992
).9.
I. M. Ryzhik and I. S. Gradshtein, Table of Integrals, Series, and Products (Academic, New York, 1965).
10.
A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions (Moscow, Nauka, 1983) (in Russian).
11.
H. Bateman and A. Erdelyi, Higher Transcendental Functions (McGraw–Hill, New York, 1953).
12.
W. Koepf, Hypergeometric Summation (Braunschweig, Vieweg, 1998).
13.
W. N. Bailey, “Generalized Hypergeometric Series,” in Cambridge Tracts in Mathematics and Mathematical Physics, No. 32, edited by G. H. Hardy and E. Cunningham (Stechert-Hafner Service Agency, New York, 1964).
This content is only available via PDF.
© 2002 American Institute of Physics.
2002
American Institute of Physics
You do not currently have access to this content.
