General Formulas for Evaluation of Singular Modulus of the Complete Elliptic Integral

다국어 초록 (Multilingual Abstract)

The complete elliptic integral of the first kind K(k) is defined for 0 < k < 1 by K(k) := π /2Ɵ=0dƟ/√1 − k2 sin2 ƟThe real number k is called the modulus of the elliptic integral. The complementary modulus is k' = √1 − k2 (0 < k' < 1).
Let ⋋ be a positive integer. The equation K(k') = √K(k),defines a unique real number k(k') (0 < k' < 1) called the singular modulus of K(k).
In this paper, we establish certain general formulas for evaluating k(λ), by employing Ramanujan’s modular equation.

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