On Appell sequences of polynomials of Bernoulli and Euler type

Journal of Mathematical Analysis and Applications

Volumn 341, Issue 2, 2008, Pages 1295-1310

  Tempesta, Piergiulio ^a  

^a SCUOLA NORMALE SUPERIORE   (Italy)

Author keywords

Appell sequences; Finite operator theory; Generalized Bernoulli polynomials

Indexed keywords

EID: 39149129419     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.07.018     Document Type: Article

References (44)

1. Adelberg A. Universal higher order Bernoulli numbers and Kummer and related congruences. J. Number Theory 84 (2000) 119-135
2. Arnold V.I. Bernoulli-Euler up-down numbers associated with function singularities, their combinatorics and arithmetics. Duke Math. J. 63 (1991) 537-554
3. Arnold V.I. The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups. Russian Math. Surveys 47 (1992) 1-51
4. Baker A. Combinatorial and arithmetic identities based on formal group laws. Lecture Notes in Math. vol. 1298 (1987), Springer 17-34
5. Baker A., Clarke F., Ray N., and Schwartz L. On the Kummer congruences and the stable homotopy of BU. Trans. Amer. Math. Soc. 316 (1989) 385-432
6. Bernoulli J. Ars conjectandi (1713), Basel
7. Boas R.P., and Buck R.C. Polynomial Expansions of Analytic Functions (1964), Springer-Verlag, New York
8. di Bucchianico A., and Loeb D. Umbral calculus. Electron. J. Combin. DS3 (2000). http://www.combinatorics.org
9. Carlitz L. Degenerate Stirling, Bernoulli and Eulerian numbers. Util. Math. 15 (1979) 51-88
10. Carlitz L. Some theorems on Bernoulli numbers of higher order. Pacific J. Math. 2 (1952) 127-139
11. Carlitz L., and Olson F.R. Some theorems on Bernoulli and Euler numbers of higher order. Duke Math. J. 21 (1954) 405-421
12. Clarke F. The universal von Staudt theorems. Trans. Amer. Math. Soc. 315 (1989) 591-603
13. Doyon B., Lepowsky J., and Milas A. Twisted vertex operators and Bernoulli polynomials. Commun. Contemp. Math. 8 2 (2006) 247-307
14. Dilcher K., Skula L., and Slavutskii I.S.H. Bernoulli numbers. Bibliography (1713-1990). Queen's Papers in Pure and Appl. Math. vol. 87 (1991), Queen's University, Kingston, ON. http://www.mathstat.dal.ca/dilcher/~bernoulli.html iv+175 pp. (1990)
15. Dunne G.V., and Schubert C. Bernoulli number identities from quantum field theory. arXiv: (2004). math.NT/0406610
16. Eie M. A note on Bernoulli numbers and Shintani generalized Bernoulli polynomials. Trans. Amer. Math. Soc. 348 (1996) 1117-1136
17. Erdélyi A. The Bateman Manuscript Project, vol. 2 (1953), McGraw-Hill
18. Fairlie D.B., and Veselov A.P. Faulhaber and Bernoulli polynomials and solitons. Phys. D 152-153 (2001) 47-50
19. Faber C., and Pandharipande R. Hodge integrals and Gromov-Witten theory. Invent. Math. 139 (2000) 173-199
20. M.P. Grosset, P. Veselov Elliptic Faulhaber polynomials and Lamé densities of states, Int. Math. Res. Not. (2006), Article ID 62120, 31 pp
21. Hazewinkel M. Formal Groups and Applications (1978), Academic Press, New York
22. Howard F.T. Congruences and recurrences for Bernoulli numbers of higher order. Fibonacci Quart. 32 (1994) 316-328
23. Ireland K., and Rosen M. A Classical Introduction to Modern Number Theory. second ed. (1990), Springer-Verlag
24. Iwasawa K. Lectures on p-Adic L-Functions (1972), Princeton Univ. Press, Princeton
25. Koblitz N. p-Adic Numbers, p-Adic Analysis and Zeta-Functions. second ed. (1984), Springer-Verlag, New York
26. Lang S. Introduction to Modular Forms (1976), Springer-Verlag
27. Levi D., Negro J., and del Olmo M.A. Discrete derivatives and symmetries of difference equations. J. Phys. A 34 (2001) 2023-2030
28. Levi D., Tempesta P., and Winternitz P. Umbral calculus, difference equations and the discrete Schrödinger equation. J. Math. Phys. 45 (2004) 4077-4105
29. Levi D., Tempesta P., and Winternitz P. Lorentz and Galilei invariance on lattices. Phys. Rev. D 69 (2004) 105011
30. S. Marmi, P. Tempesta, Polylogarithms, hyperfunctions and generalized Lipschitz summation formulae, Preprint 1-2007, Centro di ricerca matematica Ennio De Giorgi, Scuola Normale Superiore, Pisa, 2007
31. 1-transfer. Current Trends in Algebraic Topology 2 (1982), CMS-Amer. Math. Soc. part 2, pp. 437-449
32. Phillips G.M. Interpolation and Approximation by Polynomials. CMS Books Math. vol. 14 (2003), Springer-Verlag
33. Ray N. Stirling and Bernoulli numbers for complex oriented homology theory. In: Carlsson G., Cohen R.L., Miller H.R., and Ravenel D.C. (Eds). Algebraic Topology. Lecture Notes in Math. vol. 1370 (1986), Springer-Verlag 362-373
34. Riordan J. An Introduction to Combinatorial Analysis (1958), Wiley, New York
35. Roman S. The Umbral Calculus (1984), Academic Press, New York
36. Rota G.C. Finite Operator Calculus (1975), Academic Press, New York
37. Slavutskii I.Sh. Outline of the history of research on the arithmetic properties of Bernoulli numbers. Istor.-Mat. Issled. 32/33 (1990) 158-181 (in Russian)
38. Smirnov Y., and Turbiner A. Lie algebraic discretization of differential operators. Modern Phys. Lett. A 10 (1995) 1795-1802
39. Tempesta P. Formal groups, Bernoulli-type polynomials and L-series. C. R. Math. Acad. Sci. Paris Ser. I 345 (2007) 303-306
40. P. Tempesta, Dirichlet and Riemann Hurwitz zeta functions associated with formal groups and generalized Bernoulli polynomials, preprint, 2007
41. Turbiner A. Canonical discretization I. Different faces of the (an)harmonic oscillator. Internat. J. Modern Phys. A 16 (2001) 1579-1603
42. Washington L.C. Introduction to Cyclotomic Fields. second ed. (1997), Springer-Verlag
43. Young P.T. Congruences for Bernoulli, Euler and Stirling numbers. J. Number Theory 78 (1999) 204-227
44. Zagier D. Valeurs des fonctions zêta des corps quadratiques réels aux entiers négatifs. Astérisque 41-42 (1977) 135-151