Formal power series of logarithmic type

DOI10.1016/0001-8708(89)90079-0zbMath0688.05001OpenAlexW1990741252MaRDI QIDQ1263588

Gian-Carlo Rota, Daniel E. Loeb

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0001-8708(89)90079-0

zbMATH Keywords

Roman coefficientsharmonic logarithms

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Factorials, binomial coefficients, combinatorial functions (05A10)

Related Items

The Roman harmonic numbers revisited ⋮ Some Explanations of Dobinski's Formula ⋮ Global series for height 1 multiple zeta functions ⋮ Exponential-type extended Riordan arrays and reciprocity law for generalized Stirling numbers ⋮ Factorial functions and Stirling numbers of fractional orders ⋮ The iterated logarithmic algebra ⋮ Factorials and Stirling numbers in the algebra of formal Laurent series ⋮ Initial value problems in the logarithmic algebra ⋮ Sets with a negative number of elements ⋮ Coalgebraic foundations of the method of divided differences ⋮ A generalization of the Stirling numbers ⋮ Motivic information ⋮ The harmonic logarithms and the binomial formula ⋮ Umbral presentations for polynomial sequences ⋮ Postmodern logarithmo-technia ⋮ Combinatorial snapshots. ⋮ Umbral calculus and its applications. A special issue dedicated to Gian-Carlo Rota. Proceedings of the meeting, Cortona, Italy, June 21--26, 1998 ⋮ Some combinatorial conjectures regarding the classical Chu- Vandermonde formula ⋮ The classical umbral calculus and the flow of a Drinfeld module ⋮ The umbral transfer-matrix method. I: Foundations ⋮ The algebraic properties of the generalized Pascal functional matrices associated with the exponential families ⋮ Shifts and periodicity in algebraic analysis ⋮ Compositional calculus

Cites Work

• The theory of the umbral calculus. II
• The theory of the umbral calculus. III
• An Appell cross-sequence suggested by the Bernoulli and Euler polynomials of general order
• Dual operators and Lagrange inversion in several variables
• Two identities in the theory of polynomials of binomial type
• Extensions of umbral calculus: Penumbral coalgebras and generalized Bernoulli numbers
• Umbral calculus and special functions
• More on the umbral calculus, with emphasis on the \(q\)-umbral calculus
• Some comments on Rota's umbral calculus
• Integration in the umbral calculus
• Polynomial sequences of integral type
• The algebra for formal series. II: Sheffer sequences
• A semigroup and Gaussian polynomials
• The theory of the umbral calculus. I
• Banach algebras, logarithms, and polynomials of convolution type
• The umbral calculus
• The algebra of formal series
• Recursive matrices and umbral calculus
• On the foundations of combinatorial theory. VIII: Finite operator calculus
• On a dual relation for addition formulas of additive groups, I
• On a dual relation for addition formulas of additive groups II
• Coalgebras and Bialgebras in Combinatorics
• Multivariate Sequences of Binomial Type
• A New Expression for Umbral Operators and Power Series Inversion
• The Combinatorics of Polynomial Sequences
• Lagrange inversion in higher dimensions and umbral operators
• An exposá of the mullin-rota theory of polynomials of binomial type
• A generalisation of Turán's main theorems to binomials and logarithms
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item