2,323 research outputs found
Evaluations of series of the -Watson, -Dixon, and -Whipple type
Using -series identities and series rearrangement, we establish several
extensions of -Watson formulas with two extra integer parameters. Then they
and Sears' transformation formula are utilized to derive some generalizations
of -Dixon formulas and -Whipple formulas with two extra integer
parameters. As special cases of these results, many interesting evaluations of
series of -Watson,-Dixon, and -Whipple type are displayed
Generalizations of Ramanujan's reciprocity formula and the Askey-Wilson integral
By using two known transformation formulas for basic hypergeometric series,
we establish a direct extension of Bailey's -series identity.
Subsequently, it and Milne's identity are employed to drive multi-variable
generalizations of Ramanujan's reciprocity formula. Then we utilize also
Milne's identity to deduce a multi-variable generalization of the Askey-Wilson
integral
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