On summation formulas due to Plana, Lindelof and Abel, and related Gauss-Christoffel rules, II

被引:9
作者
Dahlquist, G [1 ]
机构
[1] Royal Inst Technol, NADA, S-10044 Stockholm, Sweden
来源
BIT | 1997年 / 37卷 / 04期
关键词
Euler Number; Summation Formula; Decimal Digit; Comparison Series; Euler Polynomial;
D O I
10.1007/BF02510353
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
This part contains Chapter 3 (of 5), which is mainly concerned with the derivation, analysis and applications of a summation formula, due to Lindelof, for alternating series and complex power series, including ill-conditioned power series. An appendix is devoted to complete monotonicity and related questions. The reader is referred to Part I (in this volume of BIT) for the abstract, the contents and the bibliography of the whole work. A short list of references for this part is at the end of this part.
引用
收藏
页码:804 / 832
页数:29
相关论文
共 13 条
[1]  
Abramowitz M, 1968, HDB MATH FUNCTIONS
[2]  
[Anonymous], 1941, LAPLACE TRANSFORM
[3]   PI, EULER NUMBERS, AND ASYMPTOTIC EXPANSIONS [J].
BORWEIN, JM ;
BORWEIN, PB ;
DILCHER, K .
AMERICAN MATHEMATICAL MONTHLY, 1989, 96 (08) :681-687
[4]   BERNOULLI AND EULER NUMBERS AND ORTHOGONAL POLYNOMIALS [J].
CARLITZ, L .
DUKE MATHEMATICAL JOURNAL, 1959, 26 (01) :1-15
[5]  
Dahlquist G., 1974, NUMERICAL METHODS
[6]  
DAHLQUIST G, 1965, BIT, V5, P1
[7]  
FETTIS H. E., 1955, MTAC, V9, P85, DOI [10.2307/2002063, DOI 10.2307/2002063]
[8]   CONVERGENCE ACCELERATION ON A GENERAL-CLASS OF POWER-SERIES [J].
GUSTAFSON, SA .
COMPUTING, 1978, 21 (01) :53-69
[9]  
Hardy G. H., 1949, Divergent Series
[10]  
LINDELOF E, 1905, CALCUL RESIDUS SES A