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R. Mullin, G.-C. Rota (1970)
Graph Theory and Its Applications
Steven Roman (1982)
The theory of the umbral calculus IIIJournal of Mathematical Analysis and Applications, 87
A. Kholodov (1990)
The umbral calculus and orthogonal polynomialsActa Applicandae Mathematica, 19
Steven Roman (1984)
The Umbral Calculus
O. V. Viskov (1975)
Operator characterization of generalized Appell polynomialsDokl. AN SSSR, 225
G. Rota, P. Doubilet (1975)
Finite operator calculus
G. Rota, D. Kahaner, A. Odlyzko (1973)
On the foundations of combinatorial theory. VIII. Finite operator calculusJournal of Mathematical Analysis and Applications, 42
V. Bukhshtaber, A. Kholodov (1990)
GROUPS OF FORMAL DIFFEOMORPHISMS OF THE SUPERLINE, GENERATING FUNCTIONS FOR SEQUENCES OF POLYNOMIALS, AND FUNCTIONAL EQUATIONSMathematics of The Ussr-izvestiya, 35
L. Slater, W. Rheinboldt (1966)
Generalized hypergeometric functions
D. E. Loeb and G.-C. Rota, using the operator of differentiation D, constructed the logarithmic algebra that is the generalization of the algebra of formal Laurent series. They also introduced Appell graded logarithmic sequences and binomial (basic) graded logarithmic sequences as sequences of elements of the logarithmic algebra and extended the main results of the classical umbral calculus on such sequences. We construct an algebra by an operator d that is defined by the formula (1.1). This algebra is an analog of the logarithmic algebra. Then we define sequences analogous to Boas-Buck polynomial sequences and extend the main results of the nonclassical umbral calculus on such sequences. The basic logarithmic algebra constructed by the operator of q-differentiation is considered. The analog of the q-Stirling formula is obtained.
Acta Applicandae Mathematicae – Springer Journals
Published: May 3, 2004
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