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Some properties for Appell series F₂ over finite fields

Integral Transforms and Special Functions, 2019
ABSTRACTHe et al. [Finite Fields and Their Applications 48 (2017), 289–305] introduced a finite field analogue for the Appell series F2 and derived its transformations, reduction formulas as well a...
Hainan Ma
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NEW CONGRUENCES FOR THE TRUNCATED APPELL SERIES

Bulletin of the Australian Mathematical Society
AbstractLiu [‘Supercongruences for truncated Appell series’, Colloq. Math.158(2) (2019), 255–263] and Lin and Liu [‘Congruences for the truncated Appell series $F_3$ and $F_4$ ’, Integral Transforms Spec. Funct.31(1) (2020), 10–17] confirmed four supercongruences for truncated Appell series. Motivated by their work, we give a new supercongruence for
Xiaoxia Wang, Wenjie Yu
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On some infinite series involving appell-polynomials and the functions F(z,α)—I [PDF]

Proceedings of the Indian Academy of Sciences - Section A, 1964
S.K. Rangarajan
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Appell series over finite fields and modular forms

Finite Fields and Their Applications, 2023
Mohit Tripathi
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Rigidity for Appell's Hypergeometric Series F4

Funkcialaj Ekvacioj, 2008
Appell's hypergeometric series F4 defines a multi-valued function in P2C$\\backslash$L with some hypersurface L, and then defines a local system over it. We show that the local system is physically rigid. Using this fact, we get a monodromy representation of F4 without using any analytic expression such as integral expression of F4. A condition for the
Yoshishige Haraoka, Youichi Ueno
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Appell’s hypergeometric series over finite fields

International Journal of Number Theory, 2019
We define four functions [Formula: see text] and [Formula: see text] as finite field analogues of Appell series [Formula: see text] and [Formula: see text], respectively using purely Gauss sums in the spirit of finite field hypergeometric series introduced by McCarthy.
Rupam Barman, Mohit Tripathi, Neelam Saikia   +2 more
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Transformations for Appell series over finite fields and traces of Frobenius for elliptic curves

Finite Fields and Their Applications, 2023
Gautam Kalita, Shaik Azharuddin
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F4-Appell series in p-adic settings and their connections to algebraic curves

Journal of Mathematical Analysis and Applications
Shaik Azharuddin, Gautam Kalita
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A new analytic continuation of Appell’s hypergeometric series F2

Journal of Mathematical Physics, 1976
The doubly infinite series for Appell’s function F2(α,a1,a2,b1,b2;x,y) is written in terms of four of Appell’s F3 functions. Analytic continuations are given for the F3 series, thereby allowing one to obtain a new analytic continuation for the F2 series.
Louis E. Wright, Krishan Sud
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Appellate and trial court caseload growth: A pooled time-series-cross-section analysis

Journal of Quantitative Criminology, 1987
This is an econometric study of factors behind filing growth since 1970 in state trial courts and, especially, appellate courts. The model posits two categories of variables: those affecting the supply of disputes and those affecting the costbenefit considerations of potential litigants.
Thomas B. Marvell, Carlisle E. Moody
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