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The need for a new classification of double hypergeometric series

1976/04/01 by B. C. Carlson · 1 citation
Mathematics · #Mathematical functions and polynomials #Bilateral hypergeometric series #Basic hypergeometric series #Series (stratigraphy) #Appell series #Mathematics #Hypergeometric identity #Order (exchange) #Transformation (genetics) #Lauricella hypergeometric series #Hypergeometric function of a matrix argument #Generalized hypergeometric function #Confluent hypergeometric function #Pure mathematics #Algebra over a field #Hypergeometric function

paper · doi:10.1090/s0002-9939-1976-0402138-8

openalex publication_date 1976/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21

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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