Some summations formulae in commutative Leibniz algebras with logarithms

• Autorzy: Przeworska-Rolewicz D.
• Języki publikacji: EN

Abstrakty

EN

A survey of summation formulae in commutative Leibniz algebras with logarithms is given. New results concerning generic functions and related summation formulae, which generalize well-known properties of the Bessel functions, are demonstrated.

Słowa kluczowe

EN

algebra with unit; Leibniz condition; logarithmic mapping; antilogarithmic mapping; true shift; binomial formula; harmonic logarithm; umbral calculus; generic function

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2007
• Tom: Vol. 36, no 3
• Strony: 841--857
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Przeworska-Rolewicz D.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa 10, P.O. Box 21, Poland,

Bibliografia

• LOEB, D.E. and ROTA, G.-C. (1989) Formal power series of logarithmic type. Advances in Mathematics 75, 1-118.
• PRZEWORSKA-ROLEWICZ, D. (1988) Algebraic Analysis. PWN - Polish Scientific Publishers and D. Reidel, Warszawa-Dordrecht.
• PRZEWORSKA-ROLEWICZ, D. (1996) A priori determined solutions of linear equations. Math. Japonica 44 (2), 395-412.
• PRZEWORSKA-ROLEWICZ, D. (1998) Logarithms and Antilogarithms. An Algebraic Analysis Approach. With Appendix by Z. Binderman. Kluwer Academic Publishers, Dordrecht.
• PRZEWORSKA-ROLEWICZ, D. (2000) Postmodern Logarithmo-technia. International Journal of Computers and Mathematics with Applications 41, 1143-1154.
• PRZEWORSKA-ROLEWICZ, D. (2001) True shifts revisited. Demonstratio Math. 34 (1), 111-122.
• PRZEWORSKA-ROLEWICZ, D. (2004) Power and logarithms. Fractional Calculus and Applied Analysis 7 (3), 283-296.
• PRZEWORSKA-ROLEWICZ, D. (2004) Antilogarithms of second order in algebras with logarithms and their applications to special functions. Commentationes Math., Tomus specialis in honorem Iuliani Musielak, 167-191.
• PRZEWORSKA-ROLEWICZ, D. (2005) Algebraic analysis in structures with Kaplansky-Jacobson property. Studia Math. 168 (2), 165-168.
• ROLEWICZ, S. (1969) On orbits of elements. Studia Math. 32, 17-22.
• ROTA, G.-C. (1998) Combinatorial Snapshots. The third of three Colloquium Lectures. Third Snapshot: Logarithms and the binomial theorem. Colloquium Lectures delivered at the Annual Meeting of the Amer. Math. Soc. Preprint. Baltimore, January, 1998.
• ROMAN, S. and ROTA, G.-C. (1978) The umbral calculus. Advances in Mathematics 27, 95-188.
• SHAPIRO, J.H. (1993) Composition Operators and Classical Function Theory. Springer-Verlag, New York.
• VON TROTHA, H. (1981) Structure properties of D-R spaces. Dissertationes Math. 180, Warszawa.
• VICH, R. (1987) Z Transform Theory and its Applications. D. Reidel, Dortrecht.
• WAWRZYŃCZYK, A. (1984) Group Representation and Special Functions. Examples and Problems prepared by A. Strasburger. D. Reidel and PWN -Polish Scientific Publishers, Dortrecht-Boston-Lancaster.