Convergence of the arithmetic-geometric mean procedure for the complex variables and the calculation of the complete elliptic integrals with complex modulus |
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| Authors: | Tohru Morita Tsuyoshi Horiguchi |
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| Institution: | (1) Department of Applied Science Faculty of Engineering, Tohoku University, 980 Sendai, Japan;(2) Department of Physics, Ohio University, 45701 Athens, Ohio, USA |
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| Abstract: | The convergence of the arithmetic-geometric mean procedure is checked for complex variables. The procedure is shown to be useful for the evaluation of the complete elliptic integrals of the first and second kinds with complex modulus. It is suggested that the procedure will be useful also for the numerical calculation of the elliptic integrals and the Jacobian elliptic functions with complex modulus in general. |
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