A LOWER BOUND FOR RATIONAL-APPROXIMATIONS TO PI

被引：4

作者：

HATA, M ^{[1
]}

机构：

[1] KYOTO UNIV,YOSHIDA COLL,INST MATH,KYOTO 606,JAPAN

来源：

JOURNAL OF NUMBER THEORY | 1993年 / 43卷 / 01期

关键词：

D O I：

10.1006/jnth.1993.1006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a sharp lower bound for rational approximations to π by modifying the classical approximation formula to the system ((log(1 - x))j)1 ≤ j ≤ K due to Hermite. In fact, it will he shown that π has an irrationality measure (less than) 13.398, which improves the earlier result announced by D. V. Chudnovsky and G. V. Chudnosvsky. © 1993 Academic Press Inc.

引用

页码：51 / 67

页数：17

共 12 条

[1] [Anonymous], 1953, HIGHER TRANSCENDENTA
[2] [Anonymous], 1989, THETA FUNCTIONS BOWD
[3] Beukers F., 1979, B LOND MATH SOC, V11, P268, DOI [10.1112/blms/11.3.268, DOI 10.1112/BLMS/11.3.268]
[4] CHUDNOVSKY DV, 1984, LECT NOTES MATH, V1052, P37
[5] CHUDNOVSKY GV, 1982, LECT NOTES MATH, V925, P299, DOI 10.1007/BFb0093500
[6] CHUDNOVSKY GV, 1979, CR HEBD ACAD SCI, V288, pA965
[7] DVORNICICH R, 1987, C MATH SOC J BOLYAI, V51, P637
[8] LEGENDRE TYPE POLYNOMIALS AND IRRATIONALITY MEASURES
HATA, M
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1990, 407 : 99 - 125
[9] MAHLER K, 1953, P K NED AKAD WET AMS, V56, P30
[10] MIGNOTTE M., 1974, B SOC MATH FRANCE ME, V37, P121

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