On the Lambert W function

被引:4664
作者
Corless, RM
Gonnet, GH
Hare, DEG
Jeffrey, DJ
Knuth, DE
机构
[1] UNIV WESTERN ONTARIO,DEPT APPL MATH,LONDON,ON N6A 5B7,CANADA
[2] ETH ZURICH,INST WISSENSCHAFTLICHES RECHNEN,ZURICH,SWITZERLAND
[3] UNIV WATERLOO,SYMBOL COMPUTAT GRP,WATERLOO,ON N2L 3G1,CANADA
[4] STANFORD UNIV,DEPT COMP SCI,STANFORD,CA 94305
关键词
D O I
10.1007/BF02124750
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The Lambert W function is defined to be the multivalued inverse of the function w --> we(w). It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches of W, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containing W.
引用
收藏
页码:329 / 359
页数:31
相关论文
共 72 条
[11]  
[Anonymous], 1994, FDN COMPUTER SCI
[12]  
Arnold VI., 1989, MATH METHODS CLASSIC, P520, DOI 10.1007/978-1-4757-1693-1
[13]   A NOTE ON COMPLEX ITERATION [J].
BAKER, IN ;
RIPPON, PJ .
AMERICAN MATHEMATICAL MONTHLY, 1985, 92 (07) :501-504
[14]   CONVERGENCE OF INFINITE EXPONENTIALS [J].
BAKER, IN ;
RIPPON, PJ .
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 1983, 8 (01) :179-186
[15]  
BARRY DA, 1993, J HYDROL, V142, P39
[16]  
Bellman R., 1963, DIFFERENTIAL DIFFERE
[17]  
Beyer W.H., 1987, CRC Standard Mathematical Tables, V25th ed.
[18]  
Borchardt C.W., 1860, J REINE ANGEWANDTE M, V1860, P111, DOI [10.1515/crll.1860.57.111, 10.1515/crll.1860.57.111.1,4, DOI 10.1515/CRLL.1860.57.111.1,4]
[19]  
Caratheodory C, 1954, THEORY FUNCTIONS COM
[20]  
Cayley A., 1889, Q J MATH, V23, P376, DOI 10.1017/cbo9780511703799.010