Convolution identities and lacunary recurrences for Bernoulli numbers

Journal of Number Theory

Volumn 124, Issue 1, 2007, Pages 105-122

  Agoh, Takashi ^a   Dilcher, Karl ^b  

^a TOKYO UNIVERSITY OF SCIENCE   (Japan)

^b DALHOUSIE UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33847124874     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnt.2006.08.009     Document Type: Article

References (43)

1. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions (1964), National Bureau of Standards
2. Agoh T. On the first case of Fermat's last theorem. J. Reine Angew. Math. 314 (1980) 21-28
3. Agoh T. On Bernoulli numbers, I. C. R. Math. Acad. Sci. Soc. R. Can. 10 (1988) 7-12
4. Agoh T. On Bernoulli numbers, II. Sichuan Daxue Xuebao 26 (1989) 60-65 (special issue)
5. Agoh T. Recurrences for Bernoulli and Euler polynomials and numbers. Expo. Math. 18 (2000) 197-214
6. T. Agoh, K. Dilcher, Stirling number convolutions and recurrence relations for Bernoulli numbers, preprint, 2005
7. Carlitz L. Note on the integral of the product of several Bernoulli polynomials. J. London Math. Soc. 34 (1959) 361-363
8. Carlitz L. Note on some convolved power sums. SIAM J. Math. Anal. 8 (1977) 701-709
9. Chen K.W. Sums of products of generalized Bernoulli polynomials. Pacific J. Math. 208 (2003) 39-52
10. Comtet L. Advanced Combinatorics. The Art of Finite and Infinite Expansions. revised and enlarged ed. (1974), D. Reidel Publ. Co., Dordrecht
11. Dilcher K. Sums of products of Bernoulli numbers. J. Number Theory 60 (1996) 23-41
12. Dilcher K., Skula L., and Slavutskii I.Sh. Bernoulli Numbers. Bibliography (1713-1990). Queen's Papers in Pure and Appl. Math. vol. 87 (1991), Queen's University, Kingston, Ontario. http://www.mathstat.dal.ca/~dilcher/bernoulli.html Updated on-line version:
13. Eie M. A note on Bernoulli numbers and Shintani generalized Bernoulli polynomials. Trans. Amer. Math. Soc. 348 (1996) 1117-1136
14. von Ettingshausen A. Vorlesungen über die höhere Mathematik vol. 1 (1827), C. Gerold, Vienna
15. Gelfand M.B. A note on a certain relation among Bernoulli numbers. Bashkir. Gos. Univ. Uchen. Zap. Ser. Mat. 31 (1968) 215-216 (in Russian)
16. Gessel I.M. Applications of the classical umbral calculus. Algebra Universalis 49 (2003) 397-434
17. Gessel I.M. On Miki's identity for Bernoulli numbers. J. Number Theory 110 (2005) 75-82
18. n and other similar series. Q. J. Math. 31 (1900) 241-247
19. m and other similar series. Q. J. Math. 43 (1912) 101-122
20. Gould H.W. Combinatorial Identities. revised ed. (1972), Gould Publications, Morgantown, WV
21. Graham R.L., Knuth D.E., and Patashnik O. Concrete Mathematics. second ed. (1994), Addison-Wesley Publ., Reading, MA
22. Hansen E.R. A Table of Series and Products (1975), Prentice Hall, Englewood Cliffs, NJ
23. Hardy G.H., and Wright E.M. An Introduction to the Theory of Numbers. fifth ed. (1979), Oxford Univ. Press
24. Hillman A.P., Mana P.L., and McAbee C.T. A symmetric substitute for Stirling numbers. Fibonacci Quart. 9 (1971) 51-60 73
25. Huang I.-C., and Huang S.-Y. Bernoulli numbers and polynomials via residues. J. Number Theory 76 (1999) 179-193
26. Jordan Ch. Calculus of Finite Differences. second ed. (1950), Chelsea Publ., New York
27. Kim T. Sums of products of q-Bernoulli numbers. Arch. Math. (Basel) 76 (2001) 190-195
28. Kim T., and Adiga C. Sums of products of generalized Bernoulli numbers. Int. Math. J. 5 (2004) 1-7
29. Knuth D.E. Two notes on notation. Amer. Math. Monthly 99 (1992) 403-422
30. Liu G.D., and Li R.X. Sums of products of Euler-Bernoulli-Genocchi numbers. J. Math. Res. Exposition 22 (2002) 469-475
31. Miki H. A relation between Bernoulli numbers. J. Number Theory 10 (1978) 297-302
32. Neuman C.P., and Schonbach D.I. Evaluation of sums of convolved powers using Bernoulli numbers. SIAM Rev. 19 (1977) 90-99
33. Nielsen N. Traité élémentaire des nombres de Bernoulli (1923), Gauthier-Villars, Paris
34. Nörlund N.E. Vorlesungen über Differenzenrechnung (1924), Springer, Berlin
35. Pólya G., and Szegö G. Problems and Theorems in Analysis I (1972), Springer, New York
36. Ramanujan S. Some properties of Bernoulli's numbers. J. Indian Math. Soc. 3 (1911) 219-234
37. Saalschütz L. Verkürzte Recursionsformeln für die Bernoullischen Zahlen. Z. Math. Phys. 37 (1892) 374-378
38. Sankaranarayanan A. An identity involving Riemann zeta function. Indian J. Pure Appl. Math. 18 (1987) 794-800
39. Satoh M. Sums of products of two q-Bernoulli numbers. J. Number Theory 74 (1999) 173-180
40. Sitaramachandrarao R., and Davis B. Some identities involving the Riemann zeta function, II. Indian J. Pure Appl. Math. 17 (1986) 1175-1186
41. Stern M.A. Beiträge zur Theorie der Bernoullischen und Eulerschen Zahlen. Abhandl. Gesellsch. Wiss. Göttingen Math. 23 (1878) 1-44
42. Wagstaff S.S. Ramanujan's paper on Bernoulli numbers. J. Indian Math. Soc. (N.S.) (9) 45 (1981) 49-65 (1984)
43. Zhang W.P. On the several identities of Riemann zeta-function. Chinese Sci. Bull. 36 (1991) 1852-1856