Identità Binomiali e Numeri Armonici
Chu, Wenchang ; De Donno, Livia
Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 213-235 / Harvested from Biblioteca Digitale Italiana di Matematica

Numerose identità classiche sui numeri armonici sono mostrate tramite l'operatore di derivazione di Newton ai coefficienti binomiali.

Several classical identilies on harmonic numbers are demonstrated by means of Newton's derivative operator on binomial coefficients.

Publié le : 2007-02-01
@article{BUMI_2007_8_10B_1_213_0,
     author = {Wenchang Chu and Livia De Donno},
     title = {Identit\`a Binomiali e Numeri Armonici },
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {213-235},
     zbl = {1178.05013},
     mrnumber = {2310965},
     language = {it},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_1_213_0}
}
Chu, Wenchang; De Donno, Livia. Identità Binomiali e Numeri Armonici . Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 213-235. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_1_213_0/

[1] Ahlgren, S. - Ekhad, S. B. - Ono, K. - Zeilberger, D., A binomial coefficient identity associated to a conjecture of Beukers, The Electronic J. Combinatorics, 5 (1998), #R10. | MR 1600106 | Zbl 0885.05017

[2] Ahlgren, S. - Ono, K., A Gaussian hypergeometric series evaluation and Apéry number congruences, J. Reine Angew. Math., 518 (2000), 187-212. | MR 1739404 | Zbl 0940.33002

[3] Andrews, G. E. - Uchimura, K., Identities in combinatorics IV: differentation and harmonic numbers, Utilitas Mathematica, 28 (1985), 265-269. | MR 821962 | Zbl 0595.33005

[4] Benjamin, A. T. - Preston, G. O. - Quinn, J. J., A Stirling Encounter with Harmonic Numbers, Mathematics Magazine, 75:2 (2002), 95-103. | MR 1573592

[5] Beukers, F., Another congruence for Apéry numbers, J. Number Theory, 25 (1987), 201-210. | MR 873877 | Zbl 0614.10011

[6] Chu, W., Binomial convolutions and hypergeometric identities, Rend. Circolo Mat. Palermo, XLIII (1994, serie II), 333-360. | MR 1344873 | Zbl 0835.33002

[7] Chu, W., A Binomial Coefficient Identity Associated with Beukers' Conjecture on Apéry numbers, The electronic journal of combinatorics, 11 (2004), #N15. | MR 2114196

[8] Chu, W., Harmonic Number Identities and Hermite-Padé Approximations to the Logarithm Function, Journal of Approximation Theory, 137:1 (2005), 42-56. | MR 2179622 | Zbl 1082.41014

[9] Chu, W. - De Donno, L., Hypergeometric Series and Harmonic Number Identities, Advances in Applied Mathematics, 34:1 (2005), 123-137. | MR 2102278 | Zbl 1062.05017

[10] Chu, W. - De Donno, L., Transformation on infinite double series and applications to harmonic number Identities, AAECC: Applicable Algebra in Engineering, Communication and Computing, 15:5 (2005), 339-348. | MR 2122310 | Zbl 1062.33022

[11] Comtet, L., Advanced Combinatorics, Dordrecht-Holland, The Netherlands, 1974. | MR 460128

[12] Driver, K. - Prodinger, H. - Schneider, C. - Weideman, J., Padé approximations to the logarithm II: Identities, recurrences and symbolic computation, To appear in ``The Ramanujan Journal''. | MR 2267670

[13] Driver, K. - Prodinger, H. - Schneider, C. - Weideman, J., Padé approximations to the logarithm III: Alternative methods and additional results, To appear in ``The Ramanujan Journal''. | MR 2293791

[14] Gould, H. W., Combinatorial Identities, Morgantown, 1972. | MR 354401 | Zbl 0241.05011

[15] Graham, R. L. - Knuth, D. E. - Patashnik, O., Concrete Mathematics, Addison-Wesley Publ. Company, Reading, Massachusetts, 1989. | MR 1001562

[16] Lyons, R. - Paule, P. - Riese, A., A computer proof of a series evaluation in terms of harmonic number, Appl. Algebra Engrg. Comm. Comput., 13:4 (2002), 327-333. | MR 1953199 | Zbl 1011.33003

[17] Lyons, R. - Steif, J., Stationary determinantal process: Phase multiplicity, Bernoullicity, entropy and domination, Duke Math. J., 120:3 (2003), 515-575. | MR 2030095 | Zbl 1068.82010

[18] Mortenson, E., Supercongruences between truncated F12 hypergeometric functions and their Gaussian analogs, Trans. Amer. Math. Soc., 355:3 (2002), 987-1007. | MR 1938742 | Zbl 1074.11044

[19] Mortenson, E., A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function, J. of Number theory, 99 (2003), 139-147. | MR 1957248 | Zbl 1074.11045

[20] Newton, Isaac, Mathematical Papers: Vol. III, D. T. Whiteside ed., Cambridge Univ. Press, London, 1969. | MR 263593

[21] Paule, P. - Schneider, C., Computer proofs of a new family of harmonic number identities, Adv. in Appl. Math., 31 (2003), 359-378. | MR 2001619 | Zbl 1039.11007

[22] Weideman, J. A. C., Padé approximations to the logarithm I: Derivation via differential equations, Quaestiones Mathematicae, 28 (2005), 375-390. | MR 2164379