Duplicate inverse series relations and hypergeometric evaluations with z = 1 / 4

Wenchang Chu

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 3, page 585-604
  • ISSN: 0392-4041

Abstract

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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 F 2 3 ⁢ 1 / 4 -summation formulas. Further hypergeometric evaluations with the same variable are obtained through recurrence relations.

How to cite

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Chu, Wenchang. "Duplicate inverse series relations and hypergeometric evaluations with $z=1/4$." Bollettino dell'Unione Matematica Italiana 5-B.3 (2002): 585-604. <http://eudml.org/doc/195373>.

@article{Chu2002,
abstract = {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 $_\{3\}F_\{2\}[1/4]$-summation formulas. Further hypergeometric evaluations with the same variable are obtained through recurrence relations.},
author = {Chu, Wenchang},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {585-604},
publisher = {Unione Matematica Italiana},
title = {Duplicate inverse series relations and hypergeometric evaluations with $z=1/4$},
url = {http://eudml.org/doc/195373},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Chu, Wenchang
TI - Duplicate inverse series relations and hypergeometric evaluations with $z=1/4$
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/10//
PB - Unione Matematica Italiana
VL - 5-B
IS - 3
SP - 585
EP - 604
AB - 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 $_{3}F_{2}[1/4]$-summation formulas. Further hypergeometric evaluations with the same variable are obtained through recurrence relations.
LA - eng
UR - http://eudml.org/doc/195373
ER -

References

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  1. BAILEY, W. N., Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935. Zbl0011.02303JFM61.0406.01
  2. CHU, W., A reverse derivation for Gould-Hsu inversions and comments, J. Dalian Univ. Tech., 30:3 (1990), 345-349. MR1077160
  3. CHU, W., 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. CHU, W., Symmetry on Pfaff-Saalschütz-Sheppard series, Rivista di Matematica, No. 11 (1992), 73-79; Zbl. 757:33003. Zbl0757.33003
  5. CHU, W., Inversion Techniques and Combinatorial Identities: Strange evaluations of hypergeometric series, Pure Math. & Appl. [PuMA] 4:4 (1993), 409-428; MR95j:05024 & Zbl. 815:05008. Zbl0815.05008MR95j:05024
  6. CHU, W., Inversion techniques and combinatorial identities, Boll. Unione Mat. Italiana7-B (1993), 737-760. Zbl0816.33003MR1255645
  7. CHU, W., Binomial convolutions and hypergeometric identities, Rend. Circolo Mat. Palermo (serie II) XLIII (1994), 333-360. Zbl0835.33002MR1344873
  8. CHU, W., Inversion Techniques and Combinatorial Identities: A quick introduction to hypergeometric evaluations, Math. Appl., 283 (1994), 31-57; MR96a:33006 & Zbl. 830:05006. Zbl0830.05006MR96a:33006
  9. CHU, W.- HSU, L. C., Some new applications of Gould-Hsu inversions, J. Combin. Informat. & Systems Science, 14:1 (1990), 1-4; MR92c:05018 & Zbl. 717:11007. Zbl0717.11007MR92c:05018
  10. GESSEL, I., Finding identities with the WZ method, J. Symbolic Computation, 20 (1995), 537-566. Zbl0908.33004MR1395413
  11. GESSEL, I.- STANTON, D., Strange evaluations of hypergeometric series, SIAM J. Math. Anal., 13 (1982), 295-308. Zbl0486.33003MR647127
  12. GOULD, H. W.- HSU, L. C., Some new inverse series relations, Duke Math. J., 40 (1973), 885-891. Zbl0281.05008MR337652
  13. KARLSSON, W., Clausen's hypergeometric series with variable 1/4, J. Math. Anal. & Appl., 196 (1995), 172-180. Zbl0846.33010

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