文摘
We shall study the differential equation $${y'^2} = {T_n}\left( y \right) - \left( {1 - 2{\mu ^2}} \right)$$ where μ2 is a constant, Tn(x) are the Chebyshev polynomials with n = 3, 4, 6.The solutions of the differential equations will be expressed explicitly in terms of the Weierstrass elliptic function which can be used to construct theories of elliptic functions based on 2F1(1/4, 3/4; 1; z), 2F1(1/3, 2/3; 1; z), 2F1(1/6, 5/6; 1; z) and provide a unified approach to a set of identities of Ramanujan involving these hypergeometric functions.