A New Proof of Rogers's Transformations of Infinite Series

Slater, Louise

doi:10.1112/plms/s2-53.6.460

Cited by 142 publications

(165 citation statements)

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“…The celebrated Bailey [2] transform was extensively used to obtain transformation formulae of ordinary hypergeometric series and basic hypergeometric series with help of known summation formulae. The technique provided by Bailey [2] and Slater [3], [4] motivated a number of mathematicians namely Andrews [7], [8], Verma and Jain [9], [10], U.B.Singh [12], Agarwal [13], S.P. Singh [14], Denis et.al.…”

Section: Introductionmentioning

confidence: 99%

On transformation formulae of ordinary hypergeometric series

Yadav

Kumar

Khan

2014

Global Journal of Mathematical Analysis

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Section: Introductionmentioning

confidence: 99%

On transformation formulae of ordinary hypergeometric series

Yadav

Kumar

Khan

2014

Global Journal of Mathematical Analysis

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“…From (6.13) one can easily construct α(1, n) using (2.9) and (2.2). Filling all this into (1.4), we obtain 14) which is (1.13).…”

Section: Second Extensionmentioning

confidence: 99%

Bailey Pairs With Free Parameters, Mock Theta Functions and Tubular Partitions

Andrews

2014

Ann. Comb.

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This study began in an effort to find a simpler derivation of the Bailey pairs associated with the seventh order mock theta functions. It is shown that the introduction of a new parameter independent of both a and q leads to a much simpler treatment. It is noted that a previous treatment of the central fifth order mock theta function inadvertently uses this approach. The paper concludes by applying this method to find new surprising identities and new arithmetic objects, tubular partitions.

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“…(3.5) and (3.6) follow immediately when we use the Bailey pairs, A(5) and A(8) in Slater's list [40]. See also Ref.…”

Section: The 5th Order Mock Theta Functionsmentioning

confidence: 99%

“…By applying the Bailey chain method with the pairs such as C (7) and C(5) in Slater's list [40], we obtain [39] the following;…”

Section: The 3rd Order Mock Theta Functionsmentioning

confidence: 99%