Sums of powers of roots via Bell polynomials

被引：0
|
作者：
Withers, Christopher S. [1 ]
Nadarajah, Saralees [2 ]
机构：
[1] Callaghan Innovat, Lower Hutt, New Zealand
[2] Univ Manchester, Manchester M13 9PL, Lancs, England
来源：
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2022年 / 33卷 / 05期
关键词：
Bell polynomials; generating functions; Girard's formula; NEWTON-GIRARD; FORMULAS;
D O I：
10.1080/10652469.2021.1939327
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Consider a function with a power series expansion and roots {x(n), 1 <= n < infinity}. We give two methods for obtaining the sums of powers of these roots, S-k = Sigma(infinity)(n=1)x(n)(k). The first is by expressing Girard's formula in terms of Bell polynomials. Explicit expressions are given for S-k for k <= 10. The second method is through generating functions.
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页码：388 / 399
页数：12
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