Journal of the Korean Society for Industrial and Applied Mathematics
( Vol.21 NO.3 / 2017 )



Title 


The novelty of infinite series for the complete elliptic integral of the first kind(ENG) 


Author 


A.Y. Rohedi ,E. Yahya ,Y.H. Pramono ,B. Widodo 


MSC 





Publication 





Page 


167180 Page 


Abstract 





Own Status 





Keyword 





Note 





Summary 


According to the fact that the low convergence level of the complete elliptic integral of the first kind for the
modulus which having values approach to one. In this paper we propose novelty of the complete elliptic integral
which having new infinite series that consists of new modulus introduced as own modulus function. We apply scheme
of iteration by substituting the common modulus with own modulus function into the new infinite series. We obtained
so many new exact formulas of the complete elliptic integral derived from this method correspond to the number of
iterations. On the other hand, it has been also obtained a lot of new transformation functions with the corresponding
own modulus functions. The calculation results show that the enhancement of the number of significant figures of the
new infinite series of the complete elliptic integral of the first kind corresponds to the level of quadratic
convergence. 


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