Sums of powers of roots via Bell polynomials

DOI10.1080/10652469.2021.1939327OpenAlexW3173118121MaRDI QIDQ5071334

Christopher S. Withers, Saralees Nadarajah

Publication date: 21 April 2022

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2021.1939327

zbMATH Keywords

generating functionsBell polynomialsGirard's formula

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Polynomials and rational functions of one complex variable (30C10)

Cites Work

• Analogues of Newton-Girard power-sum formulas for entire and meromorphic functions with applications to the Riemann zeta function
• Recursive sequences and Girard-Waring identities with applications in sequence transformation
• A combinatorial proof of Newton's identities
• Fredholm equations have uniformly convergent solutions
• All the trinomial roots, their powers and logarithms from the Lambert series, Bell polynomials and Fox-Wright function: illustration for genome multiplicity in survival of irradiated cells
• Combinatorial proofs of the Newton-Girard and Chapman-Costas-Santos identities
• A generalized Newton-Girard formula for monomial symmetric polynomials
• Generalized power sum and Newton-Girard identities
• Fredholm theory for arbitrary measure spaces
• Mercer's Theorem and Fredholm resolvents
• A Generalized Newton-Girard Identity
• Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
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