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A Transformation Connecting Products of Generalised Basic Hypergeometric Functions

Published online by Cambridge University Press:  20 November 2018

Arun Verma
Arun Verma*
Affiliation:
University of Alberta Edmonton
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Darling [2] in 1932 gave two types (equations 11 and 18) of transformations connecting generalised hyper geometric functions. The first was studied by Bailey [1] and extended by Sears [4] to a transformation connecting products of basic hyper geometric functions of the type r+1ϕr × r+1ϕr. In a number of papers [6, 7, 8] the author has extended these results to both unilateral and bilateral series with bases q and q1/2. The second type of transformation by Darling for a product 0F1 × 3F2 was extended by Bailey [1] to a transformation between 1F0 × r+1Fr. In the same paper Bailey mentioned the transformation of a 0ϕ1 × 3ϕ2 without proof.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 2 , June 1968 , pp. 241 - 248
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Bailey, W.N., On certain relations between hyper geometric series of higher order. Jour. London Math. Soc. 8 (1933), 100-107.Google Scholar
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3. Hahn, W., Beitrage zur theorie der Heinschen Reihen. Nachr. Math. 2 (1949), 340-379.Google Scholar
4. Jackson, F.H., On q-difference equations. Amer. Jour. Math. 32 (1910), 305-314.Google Scholar
5. Sears, D.B., Transformation of basic hypergeometric functions of any order. Proc. London Math. Soc. (2)53 (1951), 158-191.Google Scholar
6. Verma, A. and Upadhyay, M., Certain transformations of basic bilateral hypergeometric functions. Indian Jour. Math. (In press).Google Scholar
7. Verma, A.,Transformations of products of basic bilateral hypergeometric series. Proc. Nat. Inst. Sc. (India). (In press).Google Scholar
8. Verma, A., Certain transformations of products of basic hypergeometric series. (Communiceited for publication).Google Scholar