Results 111 to 120 of about 2,042 (145)

Gene regulatory programs underlying diversification of facial ligaments and tendons in zebrafish. [PDF]

open access: yesDevelopment
Roberts RR   +13 more
europepmc   +1 more source

The Saalschütz chain reactions and bilateral basic hypergeometric series

Constructive Approximation, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +5 more sources

More Semi-Finite Forms of Bilateral Basic Hypergeometric Series

Annals of Combinatorics, 2007
We prove some new semi-finite forms of bilateral basic hypergeometric series. One of them yields in a direct limit Bailey’s celebrated 6ψ6 summation formula, answering a question recently raised by Chen and Fu.
Frédéric Jouhet
openaire   +3 more sources

The basic bilateral hypergeometric series and the mock theta functions

The Ramanujan Journal, 2011
In his last letter to G. N. Hardy, S. Ramanujan introduced the mock theta functions, and he also presented mock theta functions and their identities in his last note book. G. N. Watson investigated the relations between Ramanujan's fifth order mock theta function and the function introduced by M. Lerch. In this paper, the author introduces the infinite
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Certain product theorems for bilateral hypergeometric series

Mathematical Proceedings of the Cambridge Philosophical Society, 1966
Introduction. Agarwalin 1953 ((1)) gave the most general transformations involving bilateral cognate trigonometrical series of the hypergeometric type. Later, Shukla in 1957 ((2)) gave certain relations involving the products of two bilateral hypergeometric series.
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Certain Transformations of Nearly-Poised Bilateral Hypergeometric Series of Special Type

Canadian Journal of Mathematics, 1958
A few years ago Bailey (1) gave certain transformations of both terminating and non-terminating nearly-poised hypergeometric series of the ordinary type and later on he also deduced basic analogues of some of his transformations. Recently, (3) I gave certain transformations of both ordinary and basic terminating nearly-poised bilateral hypergeometric ...
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General Transformations of Bilateral Cognate Trigonometrical Series of Ordinary Hypergeometric Type

Canadian Journal of Mathematics, 1953
Whipple [6] was the first to consider transformations connecting well-poised hypergeometric series as particular cases of relations between cognate trigonometrical series. He used contour integrals of the Barnes type to deduce such transformations. Later Sears [3] gave a systematic
openaire   +2 more sources

On the Very-well-poised Bilateral Basic Hypergeometric $_5��_5$ Series

2016
This paper has been withdrawn by the author due to some errors in the ...
Ye, Runping, Zou, Qing
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A note on the sums of certain bilateral hypergeometric series

Mathematical Proceedings of the Cambridge Philosophical Society, 1959
Some years ago M. Jackson(5) obtained the sum of a particular 3H3 series which generalized the theorems of Whipple and Watson on sums of a 3F2 series, and later she(6) deduced the sum of a particular well-poised 6H6( – 1) series. In this note sums of certain particular bilateral hypergeometric series of the same type are given.
openaire   +2 more sources

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