q-Extensions of identities of Abel-Rothe type

Discrete Mathematics

Volumn 159, Issue 1-3, 1996, Pages 161-177

  Johnson, Warren P ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011052951     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0012-365X(95)00108-9     Document Type: Article

References (19)

1. N.H. Abel, Démonstration d'une expression de laquelle la formule binome est un cas particulier. Oeuvres complètes, Christiana, 1881.
2. N.H. Abel, Sur les fonctions génératrices et leurs déterminants, Oeuvres complètes, Christiana, 1881.
3. G.E. Andrews, On the foundations of combinatorial theory, V: Eulerian differential operators, Stud. Appl. Math. 50 (1971), 345-375.
4. G.E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, (Addison-Wesley, Reading, MA, 1976).
5. J. Cigler, Operatormethoden für q-Identitäten III: Umbrale Inversion und die Lagrangesche Formel, Arch. Math. 35 (1980) 533-543.
6. L. Comtet, Advanced Combinatorics (Reidel, Dordrecht, 1974).
7. G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, Vol. 35 (Cambridge U. Press, Cambridge, 1990).
8. H.W. Gould, Some generalizations of Vandermonde's convolution, Amer. Math. Monthly 63 (1956) 84-91.
9. H.W. Gould, Final analysis of Vandermonde's convolution, Amer. Math. Monthly 64 (1957) 409-415.
10. W. Hahn, Über Orthogonalpolynome, die q-Differenzengleichungen genügen, Math. Nachr. 2 (1949) 4-34.
11. J. Hofbauer, A q-analog of the Lagrange expansion, Arch. Math. 42 (1984) 536-544.
12. F.H. Jackson, A q-generalization of Abel's series, Rend. Circolo Mat. Palermo 29 (1910) 340-346.
13. P. Kirschenhofer, Binomialfolgen, Schefferfolgen und Faktorfolgen in der q-Analysis, Österreich. Akad. Wiss. Math. -Natur. Kl. Sitzungsber. II 188 (1979) 265-315.
14. Ch. Krattenthaler, Operator Methods and Lagrange Inversion: A unified approach to Lagrange formulas, Trans. Amer. Math. Soc. 305 (1988) 431-465.
15. G.-C. Rota, D. Kahaner and A. Odlyzko, On the foundations of combinatorial theory, VIII: Finite operator calculus, J. Math. Anal. Appl. 42(3) (1973) 684-760.
16. G.-C. Rota and R. Mullin, On the foundations of combinatorial theory, III: Theory of binomial enumeration, in: Graph Theory and Its Applications (Academic Press, New York/London, 1970).
17. H.A. Rothe, Formulae de serierum reversione, Leipzig, 1793.
18. M.-P. Schützenberger, Une interprétation de certaines solutions de l'équation fonctionnelle: F(x + y) = F(x) F(y), C.R. Acad. Sci. Paris 236 (1953) 352-353.
19. Volker Strehl, Identities of Rothe-Abel-Schläfli-Hurwitz-type, Discrete Math. 99 (1992) 321-340.