Geodesic
Identità Binomiali e Numeri Armonici
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 1, pp. 213-235.

Voir la notice de l'article provenant de la source 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. 
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Chu, Wenchang; De Donno, Livia. Identità Binomiali e Numeri Armonici. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 1, pp. 213-235. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_1_a10/

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[18] E. Mortenson, Supercongruences between truncated ${}_2F_1$ hypergeometric functions and their Gaussian analogs, Trans. Amer. Math. Soc., 355:3 (2002), 987-1007. | DOI | MR | Zbl

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

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

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

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