Results 111 to 120 of about 17,253 (231)
Infinite elliptic hypergeometric series: convergence and difference equations [PDF]
, 2023 We derive finite difference equations of infinite order for theta hypergeometric series and investigate the space of their solutions. In general, such infinite series diverge, we describe some constraints on the parameters when they do converge.
Krotkov, D. I., Spiridonov, V. P.
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On the positivity and integrality of coefficients of mirror maps
Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.Abstract We present natural conjectural generalisations of the ‘positivity and integrality of mirror maps’ phenomenon, encompassing the mirror maps appearing in the Batyrev–Borisov construction of mirror Calabi–Yau complete intersections in Fano toric varieties as a special case.
Sophie Bleau, Nick Sheridan
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The need for a new classification of double hypergeometric series [PDF]
, 1976 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.
B. C. Carlson
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On Convergence of q-Series Involving ϕr+1r Basic Hypergeometric Series
Journal of Inequalities and Applications, 2009 We use inequality technique and the terminating case of the q-binomial formula to give some results on convergence of q-series involving ϕr+1r basic hypergeometric series.
Mingjin Wang, Xilai Zhao
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Mathematical Methods in the Applied Sciences, Volume 49, Issue 11, Page 12524-12538, 30 July 2026.ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
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Supercongruences for a truncated hypergeometric series
Integers, 2010 Revised ...
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The Cauchy operator for basic hypergeometric series
Advances in Applied Mathematics, 2008 We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2ϕ_1$ transformation formula and Sears' ${}_3ϕ_2$ transformation formula can be easily obtained by the symmetric property of some parameters in operator identities.
Vincent Y. B. Chen, Nancy S. S. Gu
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Transformations for hypergeometric series [PDF]
, 1973 In questo lavoro si ottengono alcune trasformazioni per le serie ipergeometriche di due variabili. Si crede che i risultati siano nuovi.In this paper we obtain some transformations for hypergeometric series of two variabiles.
Sharma, B. L., Abiodun, R. F. A.
core
Some transformations of basic hypergeometric series and their applications [PDF]
, 1980 Using Bailey’s transformation, relations between basic and basic bilateral hypergeometric series are obtained. Some interesting special cases, like identities of Rogers-Ramanujan type, summation theorems for particular basic bilateral hypergeometric ...
V. K. Jain
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Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers. [PDF]
Results Math, 2020 Guo VJW, Schlosser MJ.
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