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The need for a new classification of double hypergeometric series


Author: B. C. Carlson
Journal: Proc. Amer. Math. Soc. 56 (1976), 221-224
MSC: Primary 33A30
DOI: https://doi.org/10.1090/S0002-9939-1976-0402138-8
MathSciNet review: 0402138
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Abstract: An elementary proof is given of a linear transformation which changes a particular double hypergeometric series of order two into a series of order three. A similar transformation holds for a particular series of arbitrary order in two or more variables. The change in order provides new evidence, the most compelling to date, that the order of such a series is not a fundamental property. This conclusion undermines the accepted classification of hypergeometric series in more than one variable.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0402138-8
Article copyright: © Copyright 1976 American Mathematical Society

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