1303.0878 (Yoon Seok Choun)

Power series and integral forms of Lame equation in the Weierstrass's
form and its asymptotic behaviors    [PDF]

Yoon Seok Choun

We consider the power series expansion of Lame function in the Weierstrass's form and its integral forms applying three term recurrence formula by Choun. And we investigate how Lame functions behaves as independent variable $\xi= sn^2(z,\rho)$ goes to $\infty $ asymptotically for the cases of infinite series and polynomials. We show how to transform power series expansion of Lame function to an integral formalism mathematically in an elegant way for cases of infinite series and polynomial. And we show that integral form of Lame function involves $_2F_1$ function in itself analytically.

View original: http://arxiv.org/abs/1303.0878