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Dn Basic Hypergeometric Series
The Ramanujan Journal, 1999The purpose of this paper is the study of multiple series extensions of basic hypergeometric series related to the root system \(D_n\). The starting point in this paper is a small change in the notation of \(C_n\) and \(D_n\) series to bring them closer to \(A_n\) series.
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Special values of the hypergeometric series III
Mathematical Proceedings of the Cambridge Philosophical Society, 2001In two previous papers [7, 10] the algebraic and transcendental values of the Gauss hypergeometric seriesF(a, b; c; z) = 1+abcz1!+a(a+1)b(b+1)c(c+1)z22!+… (1·1)were investigated, for various real rational parameters a; b; c and algebraic and rational values of z ∈ (0, 1), by applying the singular values of the complete elliptic integral of the first
Zucker, I. J., Joyce, G. S.
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Orthogonal Polynomials and Hypergeometric Series
Canadian Journal of Mathematics, 1958In Part I of this paper we present a theory of Padé-approximants for Laurent series, and discuss their relation to orthogonal polynomials. For earlier results in this direction we may refer to (1 ; 7; 8). It is also indicated how this theory can be extended, for example, to matrix polynomials.
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HYPERGEOMETRIC SERIES AND ‘SET’ NUMBERS
The Quarterly Journal of Mathematics, 1941Not ...
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Quasipower and hypergeometric series — construction and evaluation
Numerical Algorithms, 1995To speed up convergence of a certain class of power series in the neighbourhood of the point \(x = 1\), the series are transformed into quasipower series, that are more complicated, but converge faster. The terms contain powers of \(x\) and Gauss hypergeometric functions with argument \(x\). The class of functions is of the form \(F(x) = \sum a_k x^k\),
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Supercongruences arising from transformations of hypergeometric series
Journal of Mathematical Analysis and Applications, 2021Ji-Cai Liu
exaly
ON ASSOCIATED HYPERGEOMETRIC SERIES
The Quarterly Journal of Mathematics, 1935openaire +2 more sources