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Verma, A.; Jain, V. K.

Transformations between basic hypergeometric series on different bases and identities of Rogers-Ramanujan type. (English) Zbl 0443.33004

J. Math. Anal. Appl. 76, 230-269 (1980).
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Cited in 22 Documents

MSC:

33C05 Classical hypergeometric functions, \({}_2F_1\)
05A19 Combinatorial identities, bijective combinatorics

Keywords:

basis hypergeometric functions; Rogers-Ramanujan identities
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Full Text: DOI

References:

[1] Agarwal, R. P.; Verma, A., Generalized basic hypergeometric series with unconnected bases, (Proc. Cambridge Philos. Soc., 63 (1967)), 181-192 · Zbl 0166.07404
[2] Andrews, G. E., On Rogers-Ramanujan type identities related to the modulus 11, (Proc. London Math. Soc. (3), 30 (1975)), 330-346 · Zbl 0301.10017
[3] Andrews, G. E., Problems and prospects for basic hypergeometric functions, (Askey, R., Theory and Application of Special Functions (1975), Academic Press: Academic Press New York) · Zbl 0342.33001
[4] Andrews, G. E., On q-analogues of the Watson and Whipple summations, SIAM J. Math. Anal., 7, 332-336 (1976) · Zbl 0339.33007
[5] Bailey, W. N., Some identities involving generalized hypergeometric series, (Proc. London Math. Soc. (2), 29 (1929)), 503-516 · JFM 55.0219.05
[6] Bailey, W. N., Generalized Hypergeometric Series (1935), Cambridge tract · Zbl 0011.02303
[7] Bailey, W. N., A transformation of nearly-poised basic hypergeometric series, J. London Math. Soc., 22, 237-240 (1947) · Zbl 0031.39201
[8] Bailey, W. N., Some identities in combinatory analysis, (Proc. London Math. Soc. (2), 49 (1947)), 421-435 · Zbl 0041.03403
[9] Bailey, W. N., Identities of the Rogers-Ramanujan type, (Proc. London Math. Soc. (2), 50 (1949)), 1-10 · Zbl 0031.39203
[10] Carlitz, L., Some formulas of F. H. Jackson, Monatsh. Math., 73, 193-198 (1969) · Zbl 0177.31102
[11] Gasper, G., Positive integrals of Bessel functions, SIAM J. Math. Anal., 6, 868-881 (1975) · Zbl 0313.33013
[12] V. K. Jain; V. K. Jain
[13] V. K. Jain; V. K. Jain · Zbl 0436.33003
[14] Rogers, L. J., On two theorems of combinatory analysis and some allied identities, (Proc. London Math. Soc. (2), 16 (1917)), 315-336 · JFM 46.0109.01
[15] Sears, D. B., On the transformation theory of basic hypergeometric functions, (Proc. London Math. Soc. (2), 53 (1951)), 158-180 · Zbl 0044.07705
[16] Slater, L. J., A new proof of Rogers’ transformations of infinite series, (Proc. London Math. Soc. (2), 53 (1951)), 460-475 · Zbl 0044.06102
[17] Slater, L. J., Further identities of the Rogers-Ramanujan type, (Proc. London Math. Soc. (2), 54 (1952)), 147-167 · Zbl 0046.27204
[18] Slater, L. J., Generalized Hypergeometric Functions (1966), Cambridge Univ. Press: Cambridge Univ. Press London/New York · Zbl 0135.28101
[19] Verma, A., Certain summation formula for basic hypergeometric series, Canad. Math. Bull., 20, 369-375 (1977) · Zbl 0379.33006
[20] Watson, G. N., A new proof of the Rogers-Ramanujan identities, J. London Math. Soc., 4, 4-9 (1929) · JFM 55.0219.09
[21] Whipple, F. J.W, Some transformations of generalized hypergeometric series, (Proc. London Math. Soc. (2), 26 (1927)), 257-272 · JFM 53.0331.03
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