Applications of the formula of Faà di Bruno: combinatorial identities and monotonic functions

DOI10.1007/s00025-021-01448-9zbMath1485.05003OpenAlexW3185789754MaRDI QIDQ2044611

Omran Kouba, Horst Alzer

Publication date: 10 August 2021

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-021-01448-9

zbMATH Keywords

infinite seriescombinatorial identitiesStirling numbersLah numbersharmonic numberscompletely monotonic functionsabsolutely monotonic functionsformula of Faà di Bruno

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Gamma, beta and polygamma functions (33B15) Monotonic functions, generalizations (26A48)

Uses Software

• DLMF

Cites Work

• Some classes of completely monotonic functions. II
• A new Faà di Bruno type formula
• The Lah Numbers and thenth Derivative of e^1/x
• On the nth Derivative of Composite Functions
• The Curious History of Faa di Bruno's Formula
• Some Absolutely Monotonic and Completely Monotonic Functions
• Prehistory of Faà   di Bruno's Formula
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