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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.21 No.3
- 발행연도
- 2017.9
- 수록면
- 167 - 180 (14page)
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초록· 키워드
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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.
목차
ABSTRACT
1. INTRODUCTION
2. EQUATIONS AND THEOREMS
3. RESULT AND DISCUSSION
4. CONCLUSIONS
REFERENCES
참고문헌 (19)
참고문헌 신청
[학술지(정기간행물)] - M.L. Glasser / 1976 / Definite Integrals of the Complete Elliptic Integral / Journal of Research of the National Bureau of Standards-B. Mathematical Sciences 80B : 313 ~ 323
[학술지(정기간행물)] - E. Salamin / 1976 / Computation of π Using Arithmetic Geometric Mean / Mathematics of Computation 30 : 565 ~ 570
[학술지(정기간행물)] - J.M. Borwein / 1984 / The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions / SIAM Review 26 : 351 ~ 366
[학술지(정기간행물)] - O.A. Karlheinz / 2011 / Comprehensive Analytical Solution of the Nonlinear Pendulum / Eur. J. Phys 32 : 479 ~ 490
[학술지(정기간행물)] - M.I. Qureshi / 2011 / Analytical Solution of Differential Equation Associated with Simple Pendulum / Gen. Math. Notes 3 : 50 ~ 58
[학술지(정기간행물)] - E. Salamin / 1976 / Computation of π Using Arithmetic Geometric Mean / Mathematics of Computation 30 : 565 ~ 570
[학술지(정기간행물)] - J.M. Borwein / 1984 / The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions / SIAM Review 26 : 351 ~ 366
[학술지(정기간행물)] - O.A. Karlheinz / 2011 / Comprehensive Analytical Solution of the Nonlinear Pendulum / Eur. J. Phys 32 : 479 ~ 490
[학술지(정기간행물)] - M.I. Qureshi / 2011 / Analytical Solution of Differential Equation Associated with Simple Pendulum / Gen. Math. Notes 3 : 50 ~ 58
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