The Gould-Hsu (1973) inverse series relations have been systematically applied to the research of hypergeometric identities. Their duplicate version is established and used to demonstrate several terminating -summation formulas. Further hypergeometric evaluations with the same variable are obtained through recurrence relations.
Le relazioni inverse di Gould-Hsu (1973) sono state applicate sistematicamente alla ricerca di identità ipergeometriche. La loro versione duplicata è stabilita ed utilizzata per dimostrare numerose formule della -serie ipergeometrica. Le ulteriori valutazioni ipergeometriche sono ottenute per mezzo di relazioni ricorrenti.
@article{BUMI_2002_8_5B_3_585_0, author = {Wenchang Chu}, title = {Duplicate inverse series relations and hypergeometric evaluations with $z=1/4$}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {5-A}, year = {2002}, pages = {585-604}, zbl = {1097.33003}, mrnumber = {1934369}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2002_8_5B_3_585_0} }
Chu, Wenchang. Duplicate inverse series relations and hypergeometric evaluations with $z=1/4$. Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002) pp. 585-604. http://gdmltest.u-ga.fr/item/BUMI_2002_8_5B_3_585_0/
[1] | JFM 61.0406.01 | Zbl 0011.02303
, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935.[2] A reverse derivation for Gould-Hsu inversions and comments, J. Dalian Univ. Tech., 30:3 (1990), 345-349. | MR 1077160
,[3] On the multivariate generalizations of Gould-Hsu inversions and applications, in A Friendly Collection of Math. Papers: Proceedings on L. C. Hsu's 70th Birthday, Jilin Univ. Press (Changchun, 1990), 123-128.
,[4] Symmetry on Pfaff-Saalschütz-Sheppard series, Rivista di Matematica, No. 11 (1992), 73-79; Zbl. 757:33003. | Zbl 0757.33003
,[5] Inversion Techniques and Combinatorial Identities: Strange evaluations of hypergeometric series, Pure Math. & Appl. [PuMA] 4:4 (1993), 409-428; MR95j:05024 & Zbl. 815:05008. | MR 95j:05024 | Zbl 0815.05008
,[6] Inversion techniques and combinatorial identities, Boll. Unione Mat. Italiana7-B (1993), 737-760. | MR 1255645 | Zbl 0816.33003
,[7] Binomial convolutions and hypergeometric identities, Rend. Circolo Mat. Palermo (serie II) XLIII (1994), 333-360. | MR 1344873 | Zbl 0835.33002
,[8] Inversion Techniques and Combinatorial Identities: A quick introduction to hypergeometric evaluations, Math. Appl., 283 (1994), 31-57; MR96a:33006 & Zbl. 830:05006. | MR 96a:33006 | Zbl 0830.05006
,[9] Some new applications of Gould-Hsu inversions, J. Combin. Informat. & Systems Science, 14:1 (1990), 1-4; MR92c:05018 & Zbl. 717:11007. | MR 92c:05018 | Zbl 0717.11007
- ,[10] Finding identities with the WZ method, J. Symbolic Computation, 20 (1995), 537-566. | MR 1395413 | Zbl 0908.33004
,[11] Strange evaluations of hypergeometric series, SIAM J. Math. Anal., 13 (1982), 295-308. | MR 647127 | Zbl 0486.33003
- ,[12] Some new inverse series relations, Duke Math. J., 40 (1973), 885-891. | MR 337652 | Zbl 0281.05008
- ,[13] Clausen's hypergeometric series with variable 1/4, J. Math. Anal. & Appl., 196 (1995), 172-180. | Zbl 0846.33010
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