摘要
We shall study the differential equation y^l2=Tn（y）-（1-2μ2）;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 （l/3, 2/3; 1; z）, 2F1 （1/6, 5/6; 1; z） and provide a unified approach to a set of identities of Rmanujan involving these hypergeometric functions.
We shall study the differential equation y^l2=Tn（y）-（1-2μ2）;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 （l/3, 2/3; 1; z）, 2F1 （1/6, 5/6; 1; z） and provide a unified approach to a set of identities of Rmanujan involving these hypergeometric functions.
