Identità Binomiali e Numeri Armonici

Wenchang Chu; Livia De Donno

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 1, page 213-235
  • ISSN: 0392-4041


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

How to cite


Chu, Wenchang, and De Donno, Livia. "Identità Binomiali e Numeri Armonici ." Bollettino dell'Unione Matematica Italiana 10-B.1 (2007): 213-235. <>.

abstract = {Numerose identità classiche sui numeri armonici sono mostrate tramite l'operatore di derivazione di Newton ai coefficienti binomiali.},
author = {Chu, Wenchang, De Donno, Livia},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {ita},
month = {2},
number = {1},
pages = {213-235},
publisher = {Unione Matematica Italiana},
title = {Identità Binomiali e Numeri Armonici },
url = {},
volume = {10-B},
year = {2007},

AU - Chu, Wenchang
AU - De Donno, Livia
TI - Identità Binomiali e Numeri Armonici
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/2//
PB - Unione Matematica Italiana
VL - 10-B
IS - 1
SP - 213
EP - 235
AB - Numerose identità classiche sui numeri armonici sono mostrate tramite l'operatore di derivazione di Newton ai coefficienti binomiali.
LA - ita
UR -
ER -


  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. Zbl0885.05017MR1600106
  2. AHLGREN, S. - ONO, K., A Gaussian hypergeometric series evaluation and Apéry number congruences, J. Reine Angew. Math., 518 (2000), 187-212. Zbl0940.33002MR1739404DOI10.1515/crll.2000.004
  3. ANDREWS, G. E. - UCHIMURA, K., Identities in combinatorics IV: differentation and harmonic numbers, Utilitas Mathematica, 28 (1985), 265-269. Zbl0595.33005MR821962
  4. BENJAMIN, A. T. - PRESTON, G. O. - QUINN, J. J., A Stirling Encounter with Harmonic Numbers, Mathematics Magazine, 75:2 (2002), 95-103. MR1573592
  5. BEUKERS, F., Another congruence for Apéry numbers, J. Number Theory, 25 (1987), 201-210. Zbl0614.10011MR873877DOI10.1016/0022-314X(87)90025-4
  6. CHU, W., Binomial convolutions and hypergeometric identities, Rend. Circolo Mat. Palermo, XLIII (1994, serie II), 333-360. Zbl0835.33002MR1344873DOI10.1007/BF02844247
  7. CHU, W., A Binomial Coefficient Identity Associated with Beukers' Conjecture on Apéry numbers, The electronic journal of combinatorics, 11 (2004), #N15. MR2114196
  8. CHU, W., Harmonic Number Identities and Hermite-Padé Approximations to the Logarithm Function, Journal of Approximation Theory, 137:1 (2005), 42-56. Zbl1082.41014MR2179622DOI10.1016/j.jat.2005.07.008
  9. CHU, W. - DE DONNO, L., Hypergeometric Series and Harmonic Number Identities, Advances in Applied Mathematics, 34:1 (2005), 123-137. Zbl1062.05017MR2102278DOI10.1016/j.aam.2004.05.003
  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. Zbl1062.33022MR2122310DOI10.1007/s00200-004-0165-5
  11. COMTET, L., Advanced Combinatorics, Dordrecht-Holland, The Netherlands, 1974. MR460128
  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''. MR2267670DOI10.1007/s11139-006-6503-4
  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''. MR2293791DOI10.1007/s11139-006-0144-5
  14. GOULD, H. W., Combinatorial Identities, Morgantown, 1972. Zbl0241.05011MR354401
  15. GRAHAM, R. L. - KNUTH, D. E. - PATASHNIK, O., Concrete Mathematics, Addison-Wesley Publ. Company, Reading, Massachusetts, 1989. MR1001562
  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. Zbl1011.33003MR1953199DOI10.1007/s00200-002-0107-z
  17. LYONS, R. - STEIF, J., Stationary determinantal process: Phase multiplicity, Bernoullicity, entropy and domination, Duke Math. J., 120:3 (2003), 515-575. Zbl1068.82010MR2030095DOI10.1215/S0012-7094-03-12032-3
  18. MORTENSON, E., Supercongruences between truncated F 1 2 hypergeometric functions and their Gaussian analogs, Trans. Amer. Math. Soc., 355:3 (2002), 987-1007. Zbl1074.11044MR1938742DOI10.1090/S0002-9947-02-03172-0
  19. MORTENSON, E., A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function, J. of Number theory, 99 (2003), 139-147. Zbl1074.11045MR1957248DOI10.1016/S0022-314X(02)00052-5
  20. NEWTON, ISAAC, Mathematical Papers: Vol. III, D. T. Whiteside ed., Cambridge Univ. Press, London, 1969. MR263593
  21. PAULE, P. - SCHNEIDER, C., Computer proofs of a new family of harmonic number identities, Adv. in Appl. Math., 31 (2003), 359-378. Zbl1039.11007MR2001619DOI10.1016/S0196-8858(03)00016-2
  22. WEIDEMAN, J. A. C., Padé approximations to the logarithm I: Derivation via differential equations, Quaestiones Mathematicae, 28 (2005), 375-390. MR2164379DOI10.2989/16073600509486135

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