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.

引用

页码：388 / 399

页数：12

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